In general, minor pieces (knights and bishops) have not been held in very high regard by top atomic chess players. Those who have sought to quantify their value have assigned such quantities as 1.5 pawns or even 1.25 pawns. In the opening, minor pieces are often gladly sacrificed for pawns if there is some positional gain to be had. However, don't throw them away lightly. Besides having a greater range and mobility than pawns, making them worth keeping in the opening and middlegame, often (but not always) a minor piece proves superior to a pawn in the endgame.
In endings where one side has a minor piece, king and pawns, and the other side has just a king and pawns, where the piece count is equal, sometimes the side with the minor piece can win by exchanging the minor piece for a key enemy pawn, thus creating a winning equal pawn endgame.
The strategy is to use the minor piece to take an enemy pawn in order to achieve a far advanced passed pawn that cannot be blocked in time by the enemy. Often, before exchanging the minor piece, an enemy passed pawn must be securely blockaded first. Sometimes the minor piece must block the pawn, and then the king comes over to relieve it. The general technique is illustrated in the following position:
8/8/3k4/p7/3K1P2/P5n1/8/8 b
Black to Move and Win
In this position, Black's win is on a razor's edge. It hinges on being able to block white's f-pawn early enough and advancing his own a-pawn far enough. Remember, once Black exchanges his knight for White's a-pawn, the resulting equal pawn endgame is decided by whose passed pawn is advanced the farthest (see King and Pawn Endings -- Equal Pawns). Play begins: 1. ... Nf5+ 2. Kc3.
8/8/3k4/p4n2/5P2/P1K5/8/8 b
Black to Move
Next, Black advances his pawn. He must not allow White to push his a-pawn to a4, since then, when Black later exchanges his knight for the a-pawn, White would be able to blockade Black's a-pawn sufficiently far from queening. So, play continues: 2. ... a4! 3. Kb2.
8/8/3k4/5n2/p4P2/P7/1K6/8 b
Black to Move
Next, Black must move his king over to the f-file to relieve his knight of blocking duty so that the knight will be free to take on a3: 3. ... Ke6 4. Ka2 Kf6 5. Kb2 Ne3 6. f5 (toughest defense) 6. ... Nc4+ 7. Kb1 Nxa3 8. Kb2 a3+ 9. Ka2 [0-1].
8/8/5k2/5P2/8/p7/K7/8 b
Black to Move
Black wins since his pawn is closer to queening (see King and Pawn Endings -- Equal Pawns.)
With a bishop instead of a knight in these endings, there are usually less opportunities to win. This is because the bishop may not be on the correct color squares to exchange itself for the key enemy pawn. For example, consider:
8/8/6b1/p7/8/4K2k/P6P/8 b
Drawn
No matter who is to move in the above diagram, the position is drawn. All White needs to do is move his pawn to a3 and keep it there. Then the bishop will never be able to take it. In fact, the position would be drawn even if the h2 pawn were gone and White was a whole bishop down! Read more on this in the chapter "Pawnitization."
However, if Black can fix a key White pawn on the correct color square, then the technique of winning with the bishop is the same as that for winning with the knight.
With a rook, these endings are much easier to win, and it usually doesn't matter which side has the more advanced pawn. This is because the rook can bully the enemy king into a far region of the board, and then swing back over take the key pawn, and then queen a pawn without it being blocked at all. Consider:
8/p6k/P6P/8/6r1/K7/8/8 b
Black to Move and Win
If Black's rook were a knight or bishop, then the above position would be hopelessly drawn. This is because if Black tried to exchange his piece for White's a-pawn, then White would actually win by blockading the Black pawn much farther from queening then the White pawn. But with the rook, Black wins by pushing the White king over to the h-file first, then taking a6, so that Black's a-pawn cannot be blockaded at all. Play begins: 1. ... Rb4 2. Ka2 Rb3 3. Ka1 Ra3+ 4. Kb2 Rd3 5. Ka2 Re3 6. Ka1 Re2 7. Kb1 Ra2 8. Kc1 Rb2 9. Kd1 Rc2 10. Ke1 Rd2 11. Kf1 Re2 12. Kg1 Rf2 13. Kh1.
8/p6k/P6P/8/8/5r2/7K b
Black to Move
Now, that the White king is far from the a-file, Black will win easily by quickly taking a6 and then queening his a-pawn: 13. ... Ra2 14. Kg1 Rxa6 15. Kf1 a5 16. Ke1 a4 17. Kd1 a3 18. Kc1 a2 etc. [0-1]. Note that connecting kings would not have saved White (see King and Queen vs. King and Pawn).