There is a place for both types of grip when doing training to hit the muscle groups from different angles or at least it feels that way
reverse grip - when your fingernails are facing you, e.g, reverse grip bench press
forward grip - the standard grip with your knuckles faing you; can also be accompanied by the "death" AKA thumbless grip when the thumbs is NOT wrapped around the bar (dangerous but exciting to watch)
neutral grip - like when you do pullups with a v-bar or rope handle attachment and your hands are facing each other
mixed grip - used by some lifters on deadlifts; one hand facing you (reverse) and the other facing away (forward)
Hope that helped.