Pronate—This is the typical overhand grip where the palm is facing down.
Typical Bench press grip
Staggered Grip—Increases the friction against your palms and thus increasing your grip strength. Place one hand in a pronated grip and the other hand in a supinated grip. Then switch your grip positions for each hand on the next set.
Excellent for dead-lifts
During a heavy lift the bicep tendon on the supinated arm is prone to tear, because of the grip (Delavier, 2006, p. 84-85)