Rook endgames are among the most common and most important endings in chess, since rooks are powerful pieces that often survive to the end of the game. The Lucena position is the canonical winning technique in K+R+P vs K+R when the pawn is not on a rook file: the winning side "builds the bridge" by using the rook to shield the king from lateral checks while the king escapes to support the pawn. The umbrella technique similarly uses the rook as a shield, here to protect the king from checks during pawn promotion. These positions demonstrate that having a passed pawn is not enough, since the rook must actively support the pawn's advance.
The Philidor position represents the defender's drawing technique in similar material. The third-rank defense places the rook on the third rank to prevent the enemy king from advancing, while staying out of the way. The Vancura position is the specific drawing technique against a rook pawn (a- or h-file), where the defender's pieces coordinate to prevent the pawn from promoting. The general principle from Tarrasch that "rooks belong behind passed pawns" applies: a rook behind your own passed pawn supports its advance, while a rook behind an enemy passed pawn can blockade it.
Rook activity is the dominant theme. The rook lift, moving along a rank to attack on a different file, is a fundamental maneuver. Active rooks are worth far more than passive ones, and doubling rooks on the same file or rank creates powerful pressure. A rook on the seventh rank invades the enemy position; "pigs on the seventh" (two rooks on the seventh rank) is often decisive. Against a back-rank weakness, where the enemy king has no escape squares, mating ideas remain relevant even in simplified positions, and giving the king a luft (an escape square) is a common prophylactic move. R vs P endgames are usually drawn unless the rook is well-placed; checking distance and minimum checking distance (typically 3+ ranks of space behind the checking rook) determine whether the defender can perpetual. The principle of restriction, which means limiting opponent pieces while improving one's own, is essential throughout.