you need to go replay Half Life 2 and pay attention to the story told through the surrounding areas, lol. Go read news paper clippings and listen to radios as they chatter and letters left on desks and such. You can do all that in Half-Life 2. There is actually an enormous backstory to both Half Life and Portal, all told entirely through secondary background items that are super missable if you don't pay attention. There is a huge, global invasion. It's called the 7-hour war, because that's how long it took for humanity to surrender. The world in Half Life 2 is really fucked, they're right in the middle of teraforming it in an awful way. Humanity has already lost in Half Life 2, we're being extinguished essentially.
The stuff about the combine in particular is pretty horrifying. The combine aren't a singular race or entity of creatures, they're genetically engineered "things" that they assimilate like the borg. The Combine are like this mix of the flood and the borg, who are slowly conquering the entire universe. They go from planet to planet, taking every resource they can and making it their own, then using that planet as a base to launch new attacks. They assimilate everything, from languages to resources like the oceans to the things that live their themselves. The combine in Half Life 2 are actually sort of the old parts of humanity and other worlds that the combine have collectively absorbed.
The portal side of the story is all a lot more light hearted, actually laugh out loud funny in lots of places. The shit that started half life was basically a response to aperture science's portal technology, as they and black mesa were rival companies. Aperture Science's portal technology, however, started as a replacement for shower curtains, because their leader, Cave Johnson, was basically senile and hit his head on the ground one day. Aperture Science began as a shower curtain manufacturer, who got into theoretical sciences looking to build better shower curtains.
