Crossbows can shoot through riot shields, helmets and soft body armour. Though, so can compound bows.

Edit: BIG crossbows can shoot through walls.

Yes, it will punch clean through solid plate armor. And as they alluded to above, knights lobbied the pope to ban crossbows from use in combat because it meant a peasant with a week's worth of training could own a knight that had trained their whole life for combat