A chess problem, also called a chess composition, is a puzzle created by the composer using chess pieces on a chessboard, which presents the solver with a particular task. For instance, a position may be given with the instruction that White is to move first, and checkmate Black in two moves against any possible defence. A chess problem fundamentally differs from over-the-board play in that the latter involves a struggle between Black and White, whereas the former involves a competition between the composer and the solver. Most positions which occur in a chess problem are unrealistic in the sense that they are very unlikely to occur in over-the-board play. There is a substantial amount of specialized jargon used in connection with chess problems.

The term chess problem is not sharply defined: there is no clear demarcation between chess compositions on the one hand and puzzle or tactical exercises on the other. In practice, however, the distinction is very clear. There are common characteristics shared by compositions in the problem section of chess magazines, in specialist chess problem magazines, and in collections of chess problems in book form.

Not every chess problem has every one of these features, but most have several:

Problems can be contrasted with tactical puzzles often found in chess columns or magazines in which the task is to find the best move or sequence of moves (usually leading to mate or gain of material) from a given position. Such puzzles are often taken from actual games, or at least have positions which look as if they could have arisen during a game, and are used for instructional purposes. Most such puzzles fail to exhibit the above features.

There are various different types of chess problems:

In all the above types of problem, castling is assumed to be allowed unless it can be proved by retrograde analysis (see below) that the rook in question or king must have previously moved. En passant captures, on the other hand, are assumed not to be legal, unless it can be proved that the pawn to be captured must have moved two squares on the previous move.

There are several other types of chess problem which do not fall into any of the above categories. Some of these are really coded mathematical problems, expressed using the geometry and pieces of the chessboard. A famous such problem is the knight's tour, in which one is to determine the path of a knight that visits each square of the board exactly once. Another is the eight queens problem, in which eight queens are to be placed on the board so that none is attacking any of the others.

Of far greater relation to standard chess problems, however, are the following, which have a rich history and have been revisited many times, with magazines, books and prizes dedicated to them: