Your full game history (if you are registered user) are saved and kept in your archive for analysis and sharing. You can access them anytime by going to your profile — just click the avatar icon on the top right. You will see the menu — chose the top item (your name) and you will see the full list of your games and results in a convenient timeline.
You can expand the grouped items (the games are grouped by week, month, and year). You can download the PGN of each game or review the game and key moment analysis.
All games have a permanent link. You can share them or even embed them on your site or blog (by clicking share).
You can also view full game history of your opponents or friends by going into their profile — just click on their avatar!