Climbing rock faces is all about friction. You must maximize the frictional force between your hands and feet, and the rock you are on. This can be done by increasing the coefficient of static friction through the materials you use and increasing the force in the direction you want.
Climbing shoes are specially designed, with high friction rubber in specially chosen places, such as on the toe and heel. They are built with a downturned toe, for precise placement, direction, and application of force against the rock.
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Climbers use chalk on their hands to make sure their hands stay dry and thus have the highest friction coefficient possible.
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The way in which a climber holds onto the hand holds on a climbing route is also all based on physics. They try to make sure that the force of them pulling is in the path of most resistance. They want to maximize the component of their pulling force that points in the direction of the path of most resistance. Because of this, grabbing onto holds that are sloped downwards is much less secure than a hold which is horizontal or angled upward is while trying to pull yourself up the rock. Any high friction, hold is best, along with one that provides the largest surface area for hand to rock contact. Again, its all about the friction.