The three branches of the trigeminal nerve are the ophthalmic, maxillary, and mandibular nerves. The maxillary nerve has branches that innervate the maxillary teeth and gingiva. The mandibular nerve has both sensory and motor branches, with the posterior division providing sensory innervation to the mandibular teeth, gingiva and other structures. The trigeminal nerve is the most important nerve for dentistry as it provides sensory innervation to the face, teeth and oral cavity.