I tend to get scientific at times, and I've had this idea in my head. I'm abandoning all of the newer ideas about the aliens, and sticking with what little bits we know about them from just the first two games. From there, I came up with some reasonable ideas to explain where the aliens came from and what they're doing here. This story is far too realistic for mainstream fiction, so prepare to see many fiction tropes thoroughly dashed.
I like to think it all could have happened.
The aliens began as the noble Aquatoids perhaps ten to twenty million years ago. Back then they were a short, slender, aquatic-benthic being with prehensile limbs that could manipulate tools, and large eyes that could see clearly in deep waters. They looked very different from the aquatoids we know today. Their intelligence and communication skills evolved to the point they began going through stages of technological progress. Now, they differed from us humans in that they started off much more slowly. Over hundreds of thousands of years, they very gradually developed an advanced society. You see, these people were naturally tenders of their environment. Their ecological tendencies were strong, and they were content to maintain most things as they were. The Aquatoids were well-situated in their environment as a highly successful apex predator, thus their evolutionary pressure was slow and they had little need to advance further. Thus, their slow progress was fueled primarily by selection of mates initially, and later by sheer boredom alone. Life was easy for them, so they focused most of their efforts on entertainment.
These creatures weren't explorers then, and they were content to live underwater. Population became problematic many times, given how uncommon it was for an aquatoid to die from any cause other than age, but they would eventually find solutions that were ecologically viable. They invented every trick in the book to stave off population growth. Thus they pretty much ignored dry land, even though there existed on their world vast continents covered in large multicellular life. It was well into their technological development that they began to see diminishing nonrenewable natural resources as a particularly important problem. For hundreds of thousands of years they had simply recycled everything, and were exceedingly conscious about resource usage. But some things just couldn't last forever, and it had been too long since they had lived without their technology. Around six to eight million years ago, it came time for them to emerge from the oceans and explore.
The continents were rich with natural resources, but they knew it would not last. The Aquatoids built domed cities on land to hold in the water, and their population began to grow, but resource costs to build and maintain these cities was high. This pressured them to seek out a more efficient way to live on land, and they began to study genetic manipulation. Their goal was to create a version of themselves that could exist on land without life support systems. This led to the discovery that they could incorporate genes from other species to achieve new and potentially useful results. Over perhaps two hundred thousand years, they developed and perfected a being, which we might call the terratoid. And thus the surface became populated by terratoids and they worked with the aquatoids to distribute resources and improve efficiency. But the study of genetics continued, and more discoveries were made. It appeared that there were more breakthroughs to be had which could further improve efficiency...
Over the next couple million years, the aliens built many servant races through genetic manipulation, and became extremely efficient, but the land resources weren't going to last forever, no matter how efficient they became. This led to the eventual discovery that it was possible to leave the planet, and that out there there were more planets. The aliens built mining posts throughout their solar system, but it was a rough start because space technology was extremely demanding on nonrenewable resources. It was worth it, they reasoned, because they had no choice. But the aliens did ravage through just about everything they dared to mine in only a few thousand years time. It was time to leave for the stars, lest they be forced to damage their beautiful planets beyond recognition.
Space travel technology was developed, but nothing like we humans imagine. The aquatoids were more than content to drift through space for many generations. They weren't trying to get anywhere, rather they were simply making a calculated move to protect and nurture their home environment. Thus over the next few million years small numbers of them drifted throughout space, gradually winding up around just about every star within several dozen parsecs. They would carefully extract useful resources from planets and develop huge vaults to store the resources for long term use. Eventually, large shipments would be sent home. Life-bearing worlds were rare gems rich with genetic material they could sample to improve their servant races.
Around three million years ago, one expedition of aquatoids happened upon Earth, and it was the first world they had come across with multicellular life since leaving home. They immediately became fascinated by its wealth of advanced multicellular life, for its land and seas were filled to the brim with all sizes of plant, animal, and fungus, many of which were very large. Earth is significantly larger than the Aquatoid's home world and has over two times the gravity, so it provided a wealth of creatures adapted to a unique planetary environment, spread over much more total surface area than they had encountered on their world. The gravity was no problem as they were benthic beings, and the water could support their frame easily. Thus they dismantled their entire expedition and made a new permanent home for themselves on Earth.
The aquatoids brought with them aquatic servants from their world, including tasoths and tentaculats. They maintained a tight leash on these creatures, however, as they wanted more than anything to preserve this lush biosphere. A servant species let loose could easily become invasive. The aliens built the giant city of T'Leth deep in the ocean on a vast plain where they could construct a large structure without disrupting the natural ecosystem. Inside the city was a microcosm of home, but outside was the natural untainted Earth. For hundreds of thousands of years the aliens very carefully exploited the important resources of the Earth in careful mining operations which prevented terrain destruction. Simultaneously, they built a large array of servant races from the creatures on Earth, and even extracted genetic material from the fossils of long-extinct creatures.
Most of the aliens' time was spent in hibernation. The most efficient resource extraction methods were very slow, and there was much waiting to be done. There was no hurry, and no sense wasting resources being lively. So they slept and dreamed, and remained in stasis most of the time.
It was perhaps twenty thousand years ago that the second expedition came to Earth. They established lines of communication with T'Leth and shared their knowledge. The second expedition had brought with them servant species from other worlds, and new technology unknown to T'Leth. This expedition was not crewed by aquatoids, but by sectoids, a variation of the terratoids built for space travel and environmental resilience. They settled down on Mars and found it much to their liking, for it had lower gravity and dimmer light. With their large eyes and weak frame, they would have found it uncomfortable to settle on Earth. But air pressure was a minor concern as they were content with pressures as low as a tenth of our air, so there were no stress issues with their domed cities.
The sectoids built a city on Mars, in what is now known as Cydonia. They mined Mars for its resources and visited Earth in short stints to take advantage of the land resources that T'Leth had been ignoring. There was a species of ape on the land which was unique among the Earth animals: these creatures would build high-tech hunting weapons out of stone, and hunt large animals to eat. The apes were hugely successful, warlike, and often squabbled with each other. They ravaged lands, hunted species to extinction, and explored in search of new lands to conquer. They were not resource conscious at all. But the sectoids merely watched these apes with interest, and did not interfere with them.
Over thousands of years the sectoids amassed a wealth of precious Elerium fuel which they stored underground on Mars. They were manufacturing this substance by bombarding Uranium with alpha and beta particles. Just like the aquatoids, the sectoids built slowly with great care to preserve the Earth's natural environment. The apes (humans) developed technological advancements rapidly compared to the much slower sectoids. And so the sectoids watched with interest, staying out of the human's sight, and occasionally taking humans for study. It was their intent to make humans into a servant race.
Human war technology grew out of hand, and the sectoids began to fear they would lose control of us. Thus they began to devise a scheme to topple our governments and convert us to anarchy, however as a backup strategy weapons were devised for defense. Through subterfuge tactics and careful application of psionic coercion, the aliens began to sway humanity to turn away and ignore them. Still, small groups of humans persisted in noticing the aliens and perceiving them as a threat. After enough alien research groups went missing, a secret intergovernment organization was built to gather data on the aliens in total secrecy and protect that data so that it could be eventually used to combat the aliens. That organization was X-Com, and it was founded some time in the late 1950s.
For the first few decades of its existence, X-Com studied the aliens and was very careful to ensure the aliens didn't know what they had found out. Slowly but surely, we began to unravel their strategies, the capabilities of their technology, and their weaknesses. We learned they navigated the Earth with levitating aerial spacecraft, and that they could sense animals psionically. We could hide research groups from them most easily by putting them underground directly beneath centers of large-brained animal activity, because the animals would provide psionic waves to mask the presence of the humans. These bases could be hidden from humans and aliens alike.
In 1999, X-Com officially became aggressive against the aliens. Advanced aircraft and weapons had been developed in secret, optimized for use against the aliens. The first attack was a huge success. An X-Com stealth fighter fired a pair of medium range ballistic missiles, each carrying a small nuclear payload, at an unsuspecting alien scout vessel from a range of 60km. The vessel did not see the attack coming and was badly damaged. It crashed into the ground and X-Com sent out a ground expedition to finish off the aliens and plunder their technology. That mission was successful and X-Com walked away with a huge prize.
X-Com assimilated alien technology rapidly in the coming weeks, but the aliens had decided that retaliatory measures were necessary. It was war. Not knowing where to find X-Com, the aliens resorted to the use of terror tactics to weaken humanity's resolve to fight them. A major city was attacked on foot, and the aliens walked the streets, shooting every human in sight. Of course X-Com showed up, but this time the aliens were ready and massive X-Com casualties were inflicted. Little actual damage was done, but the message was clear: do not attempt to fight the aliens lest there be consequences.
In the following year or so, the aliens and X-Com played a tug of war game, with the aliens using smear tactics to make X-Com look bad, and X-Com continuing to plunder more and more alien technology, gaining an ever-larger advantage over the aliens. These weapons were so much more dangerous in the hands of the warrior humans. It quickly became clear to the sectoids that they were going to be overwhelmed. A last ditch effort was made to infiltrate the top governments through direct usage of psionic control. These bold attacks quickly made it clear to every human that the aliens were our enemy, and countries began to choose sides quickly, either aligning with X-Com or surrendering to the aliens.
X-Com won the war by attacking Cydonia and killing the hive brain. The sectoids lost control of their servant races and their lines of communication were breached. The few remaining aliens on Earth were systematically hunted to extinction. But during the attack on Cydonia, a message was sent to T'Leth. Humans didn't know about T'Leth yet, and so the aquatoids would keep it that way for a time. They quickly began to wake from their sleep and build war technologies. It was preparation for a massive invasion.
In 2039, the humans had almost forgotten about the aliens. It was then that the aquatoids attacked, striking down key targets in an attempt to disrupt Earth's ability to put up a fight. Military targets were attacked, as well as logistics chains and supply warehouses. They wanted to take away our weapons. X-Com still existed, but it was running skeleton crews and was not prepared for another invasion. Governments gathered in secret and equipped X-Com quickly to enable them to fight yet another war. Unfortunately, they could not take advantage of plasma weapons technology from the last war due to Elerium shortages, and the fact that the huge stores of Elerium on Mars had not yet been found. Plasma weapons had been outlawed, and all existing weapons had been locked up in secret vaults. The technology remained in computer files but not even X-Com could use the weapons or own Elerium.
So back to war we went, but this time there were far more casualties. X-Com struggled against the aliens' sheer might, but our ability to plunder technology and wage wars proved too much for them and once again we began to gain the upper hand. It was all downhill from there. It was a close call, but we won the war and destroyed T'Leth. We discovered human/sectoid hybrids and spared them because they were around 95% human, but destroyed all other servant species. The hybrids were able to re-integrate into society for the most part but were subject to racial tensions and prejudice.
Someday perhaps we will meet the sectoids and aquatoids again. Perhaps next time, circumstances will be different.