List of chess variants

This is a list of chess variants. Many thousands of variants exist; the 2007 catalogue "The Encyclopedia of Chess Variants" estimates that there are well over 2,000, with the author noting that many more known variants were considered too trivial for inclusion. 
Chess-derived games.
These chess variants are derived from chess by changing the board, board setup, pieces, or rules.
Standard rules.
Many variants employ standard chess rules and mechanics, but vary the starting position of the pieces or number of pieces.
Standard rules and board.
Different starting position.
These variants use standard boards and pieces, but the pieces start on nontraditional squares. In most such variants, the pawns are placed on their usual squares, but the position of other pieces is either randomly determined or selected by the players. The motivation for these variants is usually to nullify established opening knowledge. The downside of these variants is that the initial position usually has less harmony and balance than the standard chess position.
Different number of pieces.
These variants use standard chess pieces on a standard board, but players begin with unorthodox numbers of pieces. For example, starting with multiple queens or fewer pawns. Many such games use unbalanced starting positions, with one player having more or fewer of particular pieces than the other player.
Standard rules on a variant board.
In these variants, the same pieces and rules as in chess are used, but the board is different; It can be smaller or larger, the shape of either the board or individual spaces can be non-square or modular, or it can even be extra-dimensional or unbounded. The movement of pieces in some variants is modified in concurrence with the geometry of the gameboard.
Variant rules with standard pieces.
These variants introduce changes in the mechanics of the game, such as movement of pieces, rules for capturing, or winning conditions, using standard chess pieces.
Variant rules, standard board and pieces.
Multimove variants.
In these variants one or both players can move more than once per turn. The board and the pieces in these variants are the same as in standard chess.
Chance and incomplete information.
In contrast to classical chess which is a game of complete information, these either have elements of chance or players do not have perfect information as to the state of the board.
Nontraditional (fairy) pieces.
Fairy pieces on a standard board.
Most of the pieces in these variants are borrowed from chess. The game goal and rules are also very similar to those in chess; however, these variants include one or more fairy pieces which move differently from chess pieces.
Empress, amazon, or princess pieces.
There are a number of variants which use the empress (rook + knight) and princess (bishop + knight) compound pieces. The empress is also called marshall or chancellor. The princess is also called cardinal, archbishop, janus, paladin, or minister. Another compound piece is the amazon (queen + knight). To adapt to the new pieces, the board is usually extended to 10×8 or 10×10 with additional pawns added.
Other fairy pieces.
The pieces in these variants are borrowed from both chess and another game. The game goal and rules are either the same or very similar to those in chess. However, these variants include one or more fairy pieces which move differently from chess pieces.
Movement in higher dimensions.
A number of variants have been developed where the playing area is in three dimensions or more. In most cases an extra spatial dimension is represented by multiple boards being laid next to each other. Some extra-dimensional variants attempt to reflect the 3D nature of modern warfare (e.g. "Raumschach", designed to reflect aerial and submarine warfare), while others incorporate fantasy or science fiction ideas such as parallel worlds and time travel. An example of the latter is the 2020 computer game "5D Chess with Multiverse Time Travel".
Single-player variants.
Similar to solitaire, there are a few chess variants for a single player. Unlike chess puzzles, these variants have a random starting position. Some of these are similar to permutation chess problems, for example the game Queen's Quadrille, which was invented by Karen Robinson in 1998. All chess pieces (except pawns) are randomly placed on a 4×4 board. Then one of the queens is removed and the game is started. Pieces move as usual, however capturing is not allowed. A player can move white and black pieces in any order, without regard for colour. The goal is to move the queen along a predetermined pattern; for example from one corner to the other, or visit all squares on the board only once. The same idea is found in the game Hippodrome, which was invented by Andy Lewicki in 2003. The initial position is obtained by placing four knights on the first row and all other pieces from a chess set (except pawns) on the remaining fields. Then one of the pieces (except knights) is removed and the game is started. The goal is to move all knights to the opposite rank.
In 1998 Robinson also invented a game which Hans Bodlaender named Chess Contradance, as the setup is like a contradance with the two lines facing each other. The pieces are set up as in regular chess, but without pawns. The first and eighth ranks are safe havens, i.e., no piece can be captured on these ranks. The objective of the puzzle is to move the pieces such that all pieces move to the opposite back row without ever putting any piece in danger of being captured. Black and White alternate moves.
Games inspired by chess.
These variants are very different from chess and may be classified as abstract strategy board games instead of chess variants.
Chess-related historical and regional games.
Some of these games have developed independently while others are ancestors or relatives of modern chess. The popularity of these variants may be limited to their respective places of origin (as is largely the case for shogi), or worldwide (as is the case for xiangqi). The games have their own institutions and traditions.
References.
Bibliography
Further reading.
Shogi
Xiangqi
Others