Bishop vs Pawns Endgames
Bishop vs pawns endgames are deceptively tricky. A bishop can stop two connected passed pawns if it's on the right diagonal, but a single wrong move lets them through. The "wrong-coloured bishop" (a bishop that can't control the promotion square) creates notorious drawing problems.
The wrong-coloured bishop
The most important concept: if your bishop can't control the promotion square, you may not be able to win even with an extra pawn. Classic example: bishop + rook-pawn where the bishop doesn't control the corner, it's a draw because the defending king reaches the corner.
Bishop vs connected pawns
A bishop can usually stop two connected passed pawns if it sits on the right diagonal. But three connected pawns on the 5th rank defeat the bishop. The key: keep the pawns on the same colour as the bishop, then they block its diagonals and advance.