I have been playing a lot of Half Life (1, 2, 2: Episodes) games recently and one key aspect of all of them is the passive plot. There is a lot going on in the Half Life universe but it is not shoved down your throat, you have to work for it and often you will be in the dark and have no idea what is happening. So I recently set out to figure out what was going on while I was playing the Half Life games and what did I miss between and before the games, the following is a summery of my findings (for more detailed information check out The Half Life SAGA Story Guide).
Prior to the our first contact with the Half Life universe in Half Life original quite a lot was going on. Apature Science was developing its portal technology and GlaDOS was made operational; And the Combine Empire invades the Vortigaunts's, unseen and unnamed, homeworld. A long interplanetary war ensues and in a final desperate act they flee to Xen (the alien world that you encounter in Half Life), a "dimensional transit" station.
GMan orchestrates The Resonance Cascade by supplying the test sample that Gordan Freeman uses. The denizens of Xen notice and begin to flee to earth but the Combine has already taken notice itself. The Black Ops are sent in to clean up the incident and kill anyone they find. Barney Calhoun escapes the facility with a group of scientists (Blue Shift). A third never named race of aliens start teleporting to Black Mesa and attacking both the humans and aliens from Xen they find there; Shephard kills the Gene Worm facilitating this second invasion, and who is itself coming though a portal to Black Mesa at the time. He is then taken into custody by GMan to prevent the story of Black mesa getting out and the facility is destroyed in a nuclear explosion, originally set by the Black Ops, disarmed by Shepard, and then rearmed by GMan (Opposing Forces). By the time of the arrival of the second aliens, Gordon Freeman has already travelled to Xen and now he defeats Nihilanth, the leader of the Vortigaunts (freeing them from his slavery like absolute control), and is recruited by GMan to work for him and put into stasis, ending Half Life.
The following is a recount of the chaos that ensued between the original and Half Life 2; Sometime within this mess it is believed that the events of Portal take place. The Resonance Cascade spreads creating The Portal Storms depositing aliens from Xen all over earth. The human populations huddle together in urban areas behind fences and armed guards abandoning the outside world to the aliens. The Combine launch an all out assault on earth using these Portal Storms, and the Vortigaunts ally with the humans in this struggle. The Combine immediately start building their Citadels and converting humans to the Overwatch. Dr. Breen is modified and made administrator of earth, and in his first act he surrenders earth, and for the most part major opposition is ended (7 hours after the invasion started). The Survivors disperse into the country and rebel fighter groups start to form while the remaining major cities are renamed to City 1, ..., City 27, etc..
Humanity is repeatedly told that this is simply a traditional period in joining the Combine's Universal Union, but of course the Combine has already started their Borg like genocidal assimilation of the Humans and enslavement of the Vortigaunts. The Overwatch implement their Suppression Field, blocking human procreation. A chemical is put into the water to make people gradually forget the past and the Combine begin to drain earth's oceans.
Gordon Freeman returns from stasis, sent by GMan to help the rebellion. He lands a huge blow against the Combine at Nova Prospekt sparking a major rebellion. Continuing to be directed by GMan, mostly from the shadows, Gordon is successful in destabilizing the reactor of Combine's capital on earth City 17's Citadel. GMan's objective accomplished, and the Citadel about to blow leaving the Combine leaderless and fractured, GMan returns Gordon to stasis ending Half Life 2. Episode 1 starts immediately after this with GMan going back to rescue Alyx Vance but being blocked by a group of Vortigaunts who rescue her themselves, transporting her to the Citadels base and then forcing Gordon Freeman out of stasis and sending him after her. These Vortigaunts continue to block GMan from now on, severely restricting his ability to guide and communicate with both Alyx and Gordon. Before they lose the Citadel completely, the Combine set it to create a super portal and send a transmission to their homeworld asking for reinforcements. This portal is created and the request sent, destroying the Citadel in the process and ending Episode 1, but soon after the resistance is able to shut down this portal and in the process learn the location of the long missing Aperture Science research vessel, the Borealis, thought to have far advanced portal technology on board. And in the final scene of Episode 2, Eli Vance, one of the leading scientists of the resistance and Alyx's father is killed, by a newly hatched Combine advisor.
So the Combine on earth have been thrown into a fractured chaos and reinforcements from their homeworld have been delayed, but the Combine Advisors have also just entered the scene and proven to be nearly unstoppable personally and likely will prove quite effective at regaining control of the dispersed Combine forces.