The maxillary artery is a branch of the external carotid artery and supplies many structures on the face. The maxillary artery arises posterior to the mandibular neck, traverses the parotid gland, and passes forward between the sphenomandibular ligament and ramus of the mandible. It then runs a superficial course lateral to the lateral pterygoid muscle. The maxillary artery supplies deep structures of the face including the mandible, pterygoid, infratemporal fossa and segments of the pterygopalatine fossa. In this review, we will go over the anatomy and look at an in-depth view of the branches of the maxillary artery.