A drill bit includes a bit body having a face on which two different types of cutters are disposed, the first type being cutting elements suitable for drilling at least one subterranean formation and the second type being at least one of an abrasive cutting structure and an abrasive cutting element suitable for drilling through a casing shoe, reamer shoe, casing bit, casing or liner string and cementing equipment or other components, as well as cement. Methods of forming earth-boring tools include disposing at least one abrasive cutting structure or element on the earth-boring tool. Methods of drilling with earth-boring tools including drilling with at least one abrasive cutting structure or element.