There's just so much depth to it, it's amazing that some gifted people can see things to such a level so far beyond normal.

Like playing 40 games simultaneously while blindfolded, etc. And how grandmasters can remember (and can play out on the board for you move for move) thousands of games they've played. Not just the moves but the ideas behind them, which was a mistake in hindsight, other branches they could have followed instead, it's ridiculous.
Games are usually saved in .PGN format and can be read using lots of different software. I use Chessbase products, but there's lots of free things too.
The chessbase stuff is incredible.. The mega database has 4.5 million games from the 1500's to today. You can view the games, have the computer analyze, make reports, show other games from the database that started similarly, tons of things. Plus you can build an opening book from the huge database too.. So then you can see that from whatever position you're at in the game, what moves were played most often, the average rating of players that made the move, whether white or black won 55% of the time or whatever.
Also their Chessbase Magazine is great, and connects with their Chessbase software, so you can see the moves played out on the board in your normal software while the player talks about it in a video in a pane.
http://www.chessbase-shop.com/en/products/5888
Basically all the good engines (fritz, rybka, hiarcs, even opensource ones like stockfish) are modular brains that can be plugged into the main chessbase software. If you get any of the engines, they come with the software to play, analyze, etc. Then there's also the actual more expensive Chessbase 11, that lets you really dig into things, create reports, player dossiers, more of the database side of things.