The muscles in this location are usually innervated by the recurrent branch of the median nerve, except for the adductor pollicis, which is supplied by the deep branch of the ulnar nerve. They all control movement of the thumb.
Adductor pollicis draws the 1st metacarpal laterally to oppose thumb toward center of palm and rotate it medially. While frequently mention with the Thenar group it is not considered as a member of the group. It is a central muscle.
Abductor pollicis brevis abducts the thumb. This muscle is the most proximal of the thenar group.
Flexor pollicis brevis, which lies next to the abductor, will flex the thumb, curling it up in the palm.
Opponens pollicis lies deep to abductor pollicis brevis. As its name suggests it opposes the thumb, bringing it against the fingers. This is a very important movement, as most of our dexterity comes from this action.
The innervation of these muscles by the median nerve is unusual, as most of the intrinsic muscles on the palm of the hand are supplied by the ulnar nerve. The lateral two lumbrical muscles are the other exception.
Another muscle that controls movement of the thumb is adductor pollicis. It lies deeper and more distal to flexor pollicis brevis. Despite its name, its main action is mainly rotation and opposition. It is not in the thenar group of muscles, so is supplied by the ulnar nerve.
A good way to remember what muscles are in the thenar eminence is "OAF"; oafs have big thenar eminences. 'O' = opponens, 'A' = abductor, 'F' = flexor. There is only one opponens. The other two muscles each have a long partner and thus are called "brevis."
Meat-LOAF: the "M" in the word "Meat" helps you remember that the LOAF muscles of the hand are innervated by the Median Nerve
ABOF (pronounced "above") the Law muscles. The law states muscles of the hand are supplied by ulnar nerve. However, ABOF the Law muscles are supplied by MEDIAN nerve. 'AB' = abductor, 'O' = Opponens, 'F' = Flexor, Law 'L' = Lateral Lumbricals (2).