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The bishop has no restrictions in distance for each move, but is limited to diagonal movement. Bishops, like all other pieces except the knight, cannot jump over other pieces. A bishop captures by occupying the square on which an enemy piece sits. The bishops may be differentiated according to which wing they begin on, i.e. As a consequence of its diagonal movement, each bishop always remains on either the white or black squares, and so it is also common to refer to them as light-squared or dark-squared bishops.

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A rook is generally worth about two pawns more than a bishop (see Chess piece relative value and the exchange). The bishop has access to only half of the squares on the board, whereas all squares of the board are accessible to the rook. On an empty board, a rook always attacks fourteen squares, whereas a bishop attacks no more than thirteen and sometimes as few as seven, depending on how near it is to the center.

Also, a king and rook can force checkmate against a lone king, while a king and bishop cannot. In general bishops are approximately equal in strength to knights, but depending on the game situation either may have a distinct advantage. Less experienced players tend to underrate the bishop compared to the knight because the knight can reach all squares and is more adept at forking.

More experienced players understand the power of the bishop (Mednis 1990:2). Bishops usually gain in relative strength towards the endgame as more pieces are captured and more open lines become available on which they can operate. A bishop can easily influence both wings simultaneously, whereas a knight is less capable of doing so. In an open endgame, a pair of bishops is decidedly superior to either a bishop and a knight, or two knights. A player possessing a pair of bishops has a strategic weapon in the form of a long-term threat to trade down to an advantageous endgame.

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Two bishops and king can force checkmate against a lone king, whereas two knights cannot. A bishop and knight can force mate, but with far greater difficulty than two bishops. In certain positions a bishop can by itself lose a move (see triangulation and tempo), while a knight can never do so. In the middlegame, a player with only one bishop should generally place friendly pawns on squares of the color that the bishop cannot move to.

The bishop is capable of skewering or pinning a piece, while the knight can do neither. This allows the player to control squares of both colors, allows the bishop to move freely among the pawns, and helps fix enemy pawns on squares on which they can be attacked by the bishop. A bishop can in some situations hinder a knight from moving. Such a bishop is often referred to as a "good" bishop.   In these situations, the bishop is said to be "dominating" the knight. Conversely, a bishop which is impeded by friendly pawns is often referred to as a "bad bishop" (or sometimes, disparagingly, a "tall pawn").  

On the other hand, in the opening and middlegame a bishop may be hemmed in by pawns of both players, and thus be inferior to a knight which can jump over them. The black light-squared bishop in the French Defense is a notorious example of this concept. A knight check cannot be blocked but a bishop check can. However, a "bad" bishop need not always be a weakness, especially if it is outside its own pawn chains.

Furthermore, on a crowded board a knight has many tactical opportunities to fork two enemy pieces. In addition, having a "bad" bishop may be advantageous in an opposite-colored bishops endgame. A bishop can fork, but opportunities are more rare. Even if the bad bishop is passively placed, it may serve a useful defensive function; a well-known quip from GM Mihai Suba is that "Bad bishops protect good pawns." a thicket of black pawns hems in Black's bishop on c8, so Black is effectively playing with one piece fewer than White. One such example occurs in the position illustrated, which arises from the Ruy Lopez: 1.e4 e5 2. Although the black pawns also obstruct the white bishop on e2, it has many more attacking possibilities, and thus is a good bishop vis-à-vis Black's bad bishop. A bishop may be fianchettoed, for example after moving the g2 pawn to g3 and the bishop on f1 to g2.

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This can form a strong defense for the castled king on g1 and the bishop can often exert strong pressure on the long diagonal (here h1–a8). A fianchettoed bishop should generally not be given up lightly, since the resulting in the pawn formation may prove to be serious weaknesses, particularly if the king has castled on that side of the board. Nc3, doubling Black's pawns and giving him a hole on d5. There are nonetheless some modern opening lines where a fianchettoed bishop is given up for a knight in order to double the opponent's pawns, for example 1.d4 g6 2.c4 Bg7 3. 5.bxc3 f5, a sharp line originated by Roman Dzindzichashvili. An endgame in which each player has only one bishop, one controlling the dark squares and the other the light, will often result in a draw even if one player has a pawn or sometimes two more than the other. Giving up a fianchettoed queen's bishop for a knight is usually less problematic. The players tend to gain control of squares of opposite colors, and a deadlock results. For example, in Karpov–Browne, San Antonio 1972, after 1.c4 c5 2.b3 Nf6 3. In endgames with same-colored bishops, however, even a positional advantage may be enough to win (Mednis 193–34). Endgames in which each player has only one bishop (and no other pieces besides the king) and the bishops are on opposite colors are often drawn, even when one side has an extra pawn or two. Many of these positions would be a win if the bishops were on the same color.

The position from Wolf versus Leonhardt (see diagram), shows an important defensive setup. Black can make no progress, since the white bishop ties the black king to defending the pawn on g4 and it also prevents the advance ...f3 because it would simply the pawn – then either the other pawn is exchanged for the bishop (an immediate draw) or the pawn advances (an easily drawn position).