Archibald Witwicky found the Underbase Cube, where it landed in the arctic.
William Irving Witwicky served as a mechanic in the USMC during the Korean War, earning the nickname Sparkplug.
When he came home, his marriage fell apart, and his wife (Christine) ended up with custody of their two boys, Ben (whom Sparkplug insisted on calling "Spike"), and Ronald ("Buster"). Sparkplug drifted from job to job, eventually ending up on an oil rig owned by Blackrock Petroleum.
Spike didn't really get along with his mom or with his brother, and eventually ran away, seeking out his father. Sparkplug and his ex-wife worked out a new agreement, allowing Spike to work at the oil rig (technically, he still "lived with" his mother, but he could stay on the rig as long as he was employed).
When Spike and Sparkplug got caught up in the Transformers' war, they both made the decision to keep Ron and Christine out of it to protect them. It was Spike and Sparkplug who suggested reaching out to G.B. Blackrock and trading Cybertronian tech for fuel.
Meanwhile, Sector Seven mobilized a military unit (G.I. Joe) to deal with the "alien threat." As did the Russians and pretty much every other player in the Cold War. As the Transformer threat grew, these multinational factions grudgingly banded together under the Earth Defense Command (while still secretly working against each other --effectively crippling any chance of a unified defense of Earth).
(When the USSR collapsed, Sector Seven seized all the KGB black assets they could grab, essentially becoming the Earth's primary line of defense.)
Carly was originally studying to be a marine biologist when she and Spike first met (she's always had an interest in sci-fi, and deep-sea life was the closest she could come to studying aliens). When she met the Transformers (and realized that she could be studying actual
aliens), she switched majors to electronics and computers (and hired Spike as a tutor to ease the transition).
"Autobot City" was actually a Blackrock-owned industrial facility (far enough away from civilization that TFs could walk around in robot mode without being seen). Blackrock was proud of the fact that the City had better security than Area 51 (because a private company can pay
more than a mere government). Blackrock hired Spike, Sparkplug, Carly, and Chip Chase, and quietly rearranged his company's holdings to accomodate his extraterrestrial partners.
Over time, Carly has become Earth's greatest authority on Cybertronian "cybiology." She's figured out things that even most Transformers themselves don't know (unlike many Cybertronians, she's perfectly willing to study "black box" tech [like T-cogs] and attempt to reproduce it).
Spike and Carly married and produced Daniel. Meanwhile, Ron married Judy and produced Sam. When Sparkplug finally passed away, Ron and Spike ended up arguing over his estate (he had willed everything to Spike, but Ron['s lawyers] insisted that at least half of it was
his). Ron's portion included the possessions of Archibald Witwicky, including the glasses.
(Ron never wanted anything to do with Spike or Sparkplug [and he made sure Sam felt the same way]; they were the black sheep of the family, always going on about their crazy conspiracy theories and drifting all over the country like vagabonds. Ron was the one putting down roots and supporting his family, like a real man.)
Spike, meanwhile, is currently the director of Blackrock Security Services; a private military contractor that uses state-of-the-art technology and techniques to keep peace, provide security against terrorists and criminal groups, bolster government military operations, and provide convenient deniability for any unexplained combat that may or may not involve giant robots.
After the Decepticons were forced off Earth, the Autobots staged a covert operation to destroy the Cybertronian technology held by the EDC. the EDC threatened to seize Blackrock's assets if the Autobots did not leave Earth. Officially, the Autobots left Earth by 2000, and the EDC was dissolved. Unofficially, a small unit of Autobot scouts remained behind in hiding, supported by Blackrock's front companies.
Various temporary incursions (the RiD, Armada, Energon, and Cybertron campaigns) occured between 2000 and 2006, largely unsupported by Blackrock and actively opposed/covered up by Sector Seven. During this time, Blackrock reached out to various human allies after-the-fact, recruiting the likes of Drs. Onishi, Jones, and Suzuki (and buying out Alternergy, turning it into Blackrock Environmental Alternatives).
While Rad, Carlos, and others have benefitted from Blackrock's covert help (through scholarships and internships ["At Blackrock, we are the Human Alliance, and we look after our own"]), Alexis has instead gone rogue. Her friendship with Starscream was a life-changing event for them both, and Alexis found herself unable to stand by while Decepticon culture is exterminated (the Autobots might be benevolent imperialists, but they are imperialists nonetheless).
When the Decepticons arrived seeking the Underbase (and the Autobots realized that the Witwicky family had a connection), Spike tried to reach out to his estranged brother --even as Hubcap (trying to be a hero) was making direct contact with Sam.
After the Underbase debacle (through which Alexis actively assisted the Decepticons as an infiltrator), Sector Seven was formally dissolved by Executive Order, and NEST was formed, forging a direct alliance between the Autobots and the US military. While NEST was originally American, Optimus pushed for increased international cooperation.
After Sector Seven was dissolved, many of its former members banded together with foreign allies (ex-KGB, ex-Mossad, etc) to create their own international agency; MECH (the Military Earth Command Headquarters), believing that alien technology belonged in human hands, and under the control of those willing to use it "properly."
Currently, NEST is officially headed by an Administrator appointed by the UN Security Council, though NEST and the Director are subordinate to the leaders of any NEST signatory nations (which is why they usually end up taking orders from the Americans [in the person of William Fowler] anyway).
In theory, Optimus and the Autobots are subordinate to the Director, being "guests" on Earth. Many Autobots have problems with this (as do some humans, who respect Optimus-the-soldier more than a politically-appointed Administrator). Thus, Autobots are often placed under heavy-handed restrictions (humans get twitchy about "machines" with built-in heavy weapons being given free reign to come and go as they please).
It's all but certain that there are MECH sympathizers inside NEST.
Optimus also took steps to ensure that the Diego Garcia base is staffed by a large number of (security-cleared) Chagossian
volunteers. It's not a full repopulation, but at the moment, it's all Optimus can do --like Griffin Rock, Diego Garcia is a testbed community; a seed of the future where humans and Autobots can truly coexist openly.
Alexis is technically with NEST as a "consultant" --her Decepticon sympathies are publically-known, and the fact that Optimus has personally vouched for her is probably the only thing keeping her from being locked up and/or accidentally stepped-on. She serves as a liaison to Starscream's more moderate Decepticon faction (who accept Earth as neutral territory and share the desire to limit collateral damage).