There is no question that this is a direct sequel, and that what takes place in Half-Life 2 is a result of the events in Half-Life. The characters are more developed versions of the caricatures in Half-Life; some of the monsters are evolved versions of creatures that first came to Earth in the first game; continuity has helped us set the stage and given a key into the new world.

The player again picks up the crowbar of research scientist Gordon Freeman, who finds himself on an alien-infested Earth being picked to the bone, its resources depleted, its populace dwindling. Freeman is thrust into the unenviable role of rescuing the world from the wrong he unleashed back at Black Mesa. And a lot of people he cares about are counting on him.

Wake Up and Smell the Ashes While Valve has kept tight lipped about the plot's details, we do have a good idea of the general setting and storyline. The game's events take place 10 years after the Black Mesa incident. The scene opens with the G-Man explaining the situation to Gordon in his typically cryptic fashion.
This is the transcript from the E3 2004 presentation,

Rise and shine, Mr Freeman…rise and shine. Not that I wish to imply that you have been sleeping on the job…no one is more deserving of a rest. And all the effort in the world would have gone to waste but until…well let's just say your hour has come again. So wake up Mr Freeman, wake up and smell the ashes.

The Combine's monstrous headquaters towers into air - so massive it's visible from almost anywhere in the city.