Note in many of the following examples how we use the fact that Black's King must move, we 'waste a move' or 'play a waiting move' if we have to.
Mate with 2 Rooks Vs King

the Rooks don't need the help of the King to push the other king to the edge & mate

Mate with 1 Rook Vs King

See how the King becomes very important in this and the following mates !

Mate with 1 Queen Vs King

  • mates only on the edge
    Although the simplest, and sometimes most automatic (useful if you are running out of time), is to use the queen like the single rook above, better is to 'cut off the board' and restrict the king even further - note that in the example black could have easily accidentally stalemated with Qd6 instead of Qf7.

  • Mate with 2 Bishops Vs King

    push the King into a corner and mate there
    Notice the waiting moves forcing Black on the edge and not escaping back into the middle
    Mate with 2 Knights Vs King
    Mate cannot be forced - one might blunder into the mating position not having seen that you would be mated next move ! However if the lone King is not alone but has for example even one pawn then mate can then in fact be forced.

    Mate with 1 Bishop & 1 Knight Vs King push the King into toward the corner the Bishop controls

  • Mate with 1 Bishop Vs King not possible

  • Mate with 1 Knight Vs King not possible

    the following based on the overview in 'the Oxford Companion to CHESS'

  • 1 Rook + King Vs 1 Bishop + King
    White may win if black's King is kept in or near a corner that the Bishop controls. A high level of technique is needed.

  • 1 Rook + King Vs 1 Knight + King
    Generally drawn but might be winning chances if the knight wanders away too far from her King.

  • 2 minor pieces Vs Rook Drawn.

  • 3 minor pieces Vs Rook - 2 Bishops+Knight wins; Bishop+2 Knights draws.

  • 2 minor pieces Vs Rook draws.

  • Rook+2 Knights Vs Rook wins.

  • Rook+Knight Vs Rook draws with a couple of exceptions.

  • Rook+Bishop Vs Rook - a difficult ending though mostly black can find enough resources to draw. Can take more than 50 moves to force the win.

  • Queen Vs minor piece wins.

  • Queen Vs 2 minor pieces and white wins more often than not (note white has the Queen) according to computer studies having the 2 Bishops may draw more easily than 2 Knights(though though distinct formations are known. Can take more than 50 moves to force the win.

  • Queen Vs minor piece wins.

  • Mate with 1 Pawn Vs King
    Actually this is the soul of pawn endgames - most endgames really, because here we fight it out to see who will promote the pawn, therefore getting a Queen and mating with the Queen's help.