How was mining used to attack a castle?

Castles are, of course designed to be resistant to attack. The battlements and loopholes in the wall allowed those inside to fire at attackers from a sheltered position, the height and placement of a castle usually allowed those inside a clear view of any attackers and there were several lines of defence inside the castle. Castles could be attacked with large catapults which could throw rocks over the walls, a battering ram, usually to break through the gates and latterly canons could try to breach the walls. Ultimately, the best form of attack would be to lay siege to the castle. This meant posting soldiers all around so that no one could leave or enter and the castle would eventually run out of food and water.