Righty vs. Lefty
Watching a lefty play a righty illuminates the game of diagonals wonderfully. Almost all baseline matches of this structure follow the same pattern. The lefty is trying to hit the forehand crosscourt to the righties backhand. The righty is trying to hit the ball crosscourt to the lefties backhand. Consequently, they have many backhand to backhand rallies down the line. This is a common rally viewed in the Roger Federer-Rafael Nadal battles.
Both players are trying to entice their opponent to hit the ball crosscourt to the forehand side, and they will often hit 6 or 7 shots in a row down the line daring the opponent to hit crosscourt. Generally the player who wins these matches has one of two advantages. First, the running crosscourt forehand is a strong enough weapon to punish an opponent when he changes the direction of the rally. Or, the angle backhand is so strong that it out-hits the speed of the player trying to hit the running forehand. Look for a more thorough explanation of diagonals in other grips articles.