knowing games by heart: how do they do that?!

I was watching an interview with Ivanchuk (link below, it's a gem ) where he brilliantly recalls all his move AND all the moves he considered. It's a common theme that i noticed by masters who can with astonish ease remember multiple games (theirs and others).

On my part i study master games and it's a lot of fun. i sometimes can remember them for a day but never longer. I continue to do study those game because it's fun and instructive but it just won"t drill long term in my head.

How do they do that? Are they brain so trained that it's almost natural? What about you guys?

Interview: https://www.youtube.com/watch?v=pUgvAoTzWBA&t=405s

I remember all sorts of math stuff because I understand it. I would guess that it is similar for GMs. I don't see anything about memorizing games in books like A Guide to Chess Improvement by Dan Heisman (2010)
https://web.archive.org/web/20140708105628/http://www.chesscafe.com/text/review781.pdf
and Studying Chess Made Easy by Andrew Soltis.
https://web.archive.org/web/20140708090448/http://www.chesscafe.com/text/review750.pdf

Fragments from a discussion last year:
"... how many chess games can you replay (till the end) ..." - VimalKumarK
"I couldn't replay any although I could recognise quite a lot." - CM JamesColeman
"Good point. I could have replayed that one. Also Reti-Tartakower where White sacrifices his Q on d8 and then forces mate with a double check. So maybe 2. Both of those are rather short though." - CM JamesColeman
"Oh yeah, that one. Maybe 3 then ..." - CM JamesColeman
"There are many many must-know games for general ideas and themes but not sure of the practical value of having all of them memorised move by move all the way through to resignation?" - CM JamesColeman
"I don't think you have to have them memorized. Just playing them over, even fairly quickly will help put the patterns and ideas into your head." - Morphysrevenges
"Yes, agree with you entirely Morphysrevenges, but the OP was asking about memorised games that you can replay out at will. For me at least, that's not many." - CM JamesColeman
In case you are curious, here are some of the games that were mentioned in the January 7, 2017 discussion:
http://www.chessgames.com/perl/chessgame?gid=1233404
http://www.chessgames.com/perl/chessgame?gid=1250654
http://www.chessgames.com/perl/chessgame?gid=1259009
http://www.chessgames.com/perl/chessgame?gid=1224575
http://www.chessgames.com/perl/chessgame?gid=1132699
http://www.chessgames.com/perl/chessgame?gid=1132581
"... Memory is too valuable to be stocked with trifles. Of my fifty-seven years I have applied at least thirty to forgetting most of what I had learned or read, and since I succeeded in this I have acquired a certain ease and cheer which I should never again like to be without. If need be, I can increase my skill in Chess, if need be I can do that of which I have no idea at present. I have stored little in my memory, but I can apply that little, and it is of good use in many and varied emergencies. I keep it in order, but resist every attempt to increase its dead weight. ..." — Emanuel Lasker, Lasker’s Manual of Chess
Possibly of interest:
Simple Attacking Plans by Fred Wilson (2012)https://web.archive.org/web/20140708090402/http://www.chesscafe.com/text/review874.pdf
http://dev.jeremysilman.com/shop/pc/Simple-Attacking-Plans-77p3731.htm
Logical Chess: Move by Move by Irving Chernev (1957)
https://web.archive.org/web/20140708104437/http://www.chesscafe.com/text/logichess.pdf
The Most Instructive Games of Chess Ever Played by Irving Chernev (1965)
https://chessbookreviews.wordpress.com/tag/most-instructive-games-of-chess-ever-played/
Winning Chess by Irving Chernev and Fred Reinfeld (1948)
https://web.archive.org/web/20140708093415/http://www.chesscafe.com/text/review919.pdf
Back to Basics: Tactics by Dan Heisman (2007)
https://web.archive.org/web/20140708233537/http://www.chesscafe.com/text/review585.pdf
https://www.chess.com/article/view/book-review-back-to-basics-tactics
Discovering Chess Openings by GM John Emms (2006)
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf
Openings for Amateurs by Pete Tamburro (2014)
http://kenilworthian.blogspot.com/2014/05/review-of-pete-tamburros-openings-for.html
https://chessbookreviews.wordpress.com/tag/openings-for-amateurs/
https://www.mongoosepress.com/catalog/excerpts/openings_amateurs.pdf
Chess Endgames for Kids by Karsten Müller (2015)
https://chessbookreviews.wordpress.com/tag/chess-endgames-for-kids/
http://www.gambitbooks.com/pdfs/Chess_Endgames_for_Kids.pdf
A Guide to Chess Improvement by Dan Heisman (2010)
https://web.archive.org/web/20140708105628/http://www.chesscafe.com/text/review781.pdf
Studying Chess Made Easy by Andrew Soltis
https://web.archive.org/web/20140708090448/http://www.chesscafe.com/text/review750.pdf
Seirawan stuff:
http://seagaard.dk/review/eng/bo_beginner/ev_winning_chess.asp?KATID=BO&ID=BO-Beginner
https://web.archive.org/web/20140708092617/http://www.chesscafe.com/text/review560.pdf
https://www.chess.com/article/view/book-review-winning-chess-endings
https://web.archive.org/web/20140627132508/http://www.chesscafe.com/text/hansen173.pdf
http://www.nystar.com/tamarkin/review1.htm

but even after days, weeks, months or even years?? I also can replay my own games but at best till the day after...

I remember some key positions from my games for months. I don't get to really choose which ones though. My brain picks some that it finds interesting and I'll analyze it even in my dreams sometimes and come up with crazy ideas at times. It's pretty neat what the brain is capable of.

Anyone can memorize just about anything, given enough time or motivation.  In school, if we memorized a long poem we got bonus marks.  We also had to memorize dates for history, various items of the periodic table in science, different countries and capitals for geography, etc.  Memorizing isn't that hard, though it can be time consuming.

Things are easier when it's something you really like.  I still remember most of the secrets from games like Mario and Zelda, which I played as a kid.  It takes no effort to recall any of these items, even decades later.  Sometimes I do forget but then, when playing, I reach that particular level and I get a flash of recollection, as clear as day.  This rarely happens with the periodic table or the capitals of obscure countries.

Finally, it's worth noting that Ivanchuk is a professional.  Lawyers, for example, are able to cite legislation references and case law precisely because it is their job.  At first this takes effort to learn, but after years of practice it starts becoming intuitive, at least for the most used and most important sections and cases.  For grandmasters it is similar, and if they love chess, it's all the easier.

Now, I won't deny that supergrandmasters aren't special, and Ivanchuk is a genius at chess, but memorizing games isn't that super-human.  Many amateurs have the Opera Game memorized, for instance, and working up to longer games is fairly simple, if you put the time in.

I think it's to do with active or passive information intake. If you're studying a master game you're maybe looking at the moves for a minute or so and you're not bending your full attention onto it (unless you're better and more diligent at study than me anyway). If you're playing OTB you're scrutinizing your position for up to 5 hours in some cases and for those 5 hours it's all you're thinking about.

Additionally, I think as you 'train' your Chess muscle/brain you become better at calculating, recognizing positions and patterns (e.g. you remember, oh it was a standard advanced french opening) so you cluster the first 6-7 moves together into one data point (rather than 14 individual moves) and then when playing deeper middlegame/endgame moves you automatically only consider simple moves and so even where your brain hasn't properly recalled the full game you begin to fill in the blanks with logical captures/moves.

I was recently able to recall a full game I'd played OTB in a Rapid time control without the moves noted. This was the first time in over a year of playing OTB Chess I could do this and it was partly because the position was quite unique and interesting and the game fairly short just over 30 moves. I've not actively tried to get any better at recalling games I think it just comes in time the more you play and in particular OTB. There is 0% chance of me remembering an online game.

Like others said, you can memorize pretty much anything if the desire is there and you spend a good amount of time on it. These GM's play 10-12 hrs a day, studying games. Their whole lives are pretty much chess all day.

For example, im basketball obsessed. Ive been playing fantasy basketball since 1999. Ive lost interest these last couple years, but i used to be able to name every single player on every NBA roster. I also used to be able to recall stats from years ago without ever looking at google. I still can for the most part.