If the game has cloud saves and is activated (which is the default)
Not all games have cloud saves, especially older games.
You will be able to continue your progress on games that have the cloud. You may have to import the saves, I'm not sure.
For the games that don't have the cloud, you are out of luck. You can check if a game has the steam cloud by looking at its properties, or going to its store page.

Been away for a bit, but sneaking back in.
Gaming on: PS4, PC, 3DS. Got a Switch! Mainly to play Smash







