The three primary gluteal muscles (maximus, medius, and minimus), in addition to the tensor fasciae latae (lateral to the primary muscles), comprise the gluteal group, which provides the majority of the support and movement that allows humans to walk upright, rotate our legs, and support our torso.
Each individual muscle is often involved in many different movements, though not always as the primary player. All four gluteal muscles originate from the outer ilium (the back of the "wings" on the pelvis). This is known as the gluteal surface.
Gluteus maximus: (Top Left) The largest muscle in the body. Supports the pelvis, lower torso, and allows the body to remain upright and regain position after stopping movement. Despite claims to the contrary, the gluteus maximus is not what gives the majority of the shape to the buttocks - that's largely determined by the panniculus adiposus ("hanging fat") of the buttocks. However, exercising the gluteus maximus may cause fat loss, which gives the impression that it is the primary progenitor of the shape.
Gluteus medius: (Top Center) Originates right below the gluteus maximus. Responsible for abducting the leg and maintaining an upright position while on one leg, such as during running, dancing, or entering a car.
Gluteus minimus: (Top Right) The smallest of the three primary gluteals, works in concert with the gluteus medius to maintain an upright position on one leg, as well as allowing the leg to turn inwards and outwards (medial rotation).
Tensor fasciae latae: (Bottom; near sartorus muscle) Located on the outside edge of the thigh, lateral to the primary gluteals. Causes knee extension, and functions to cause the primary movements during walking. Supported by the gluteus maximus. Used extensively in horseback riding.
Images:
Top: Posterior muscles of the gluteal and thigh region. Gluteus maximus, medius, and minimus highlighted. From Anatomy, Descriptive and Applied. Henry Gray, 1913. Highlighted by Mikael Haggstrom.
Bottom: Structures surrounding the right hip joint, including gluteal muscles. From Anatomy, Descriptive and Applied. Henry Gray, 1908.