How many turns can a chess game take at maximum?

Question

The shortest number of moves that a game of chess can have is 2, as far as I know:

• White moves pawn from f2 to f3, black moves pawn from e7 to e5
• White moves pawn from g2 to g4, black moves queen from d8 to h4. Checkmate.

Which results in this situation:

There might be more games which end after 2 rounds, but as far as I know there is no game with fewer rounds / moves.

How many moves do the longest games take?

I thought I have read that the number is about 8000 moves.

A finite maximum number exists, because of the fifty-move rule and threefold repetition and I assume that players claim draw by those rules if possible.

Please link also to the source of your information!

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edit: Jacob Schlather mentioned a blogpost with this information

[...] The Belgrade Marathon was a contest between Ivan Nicolic and Goran Arsovic that lasted over 20 hours and ended in a draw after 269 moves due to the so-called “50 Move Rule”, [...]

Source: The Longest Possible Chess Game

So the longest game that was actually played took at least 269 moves. Later he explains how he comes to 5,870 possible chess moves.

Answer 1

Each of the 16 pawns can move at most 6 times and there are 30 captures possible. Therefore $(16\cdot6+30)\cdot 50=6300$ is a rough upper bound (for example, not all pawns can make it to the opposite line without sometimes capturing - which would mean that sometimes pawn move and capture occur together).

Answer 2

There is no upper bound on the length of a legal chess game. All that is required is for the game to reach a position where the threefold repetition rule would apply, and for neither player to claim the draw. The same position could recur over and over, and so long as neither player claims the draw, the game can continue indefinitely.