Its common English name, sunfish, refers to the animal's habit of sunbathing at the surface of the sea. Its common names in Dutch, Portuguese, French, Spanish, Catalan, Italian, Russian, Greek, Hungarian, Norwegian, and German (maanvis, peixe lua, Poisson lune, pez luna, peix lluna, Pesce luna, рыба-луна, φεγγαρόψαρο, holdhal, månefisk and Mondfisch, respectively) mean "moon fish", in reference to its rounded shape. In German, the fish is also known as Schwimmender Kopf, or "swimming head". In Polish, it is named samogłów, meaning "head alone" or "only head", because it has no true tail. In Swedish and Danish it is known as klumpfisk, in Dutch klompvis, in Finnish möhkäkala, all of which mean "lump fish". The Chinese translation of its academic name is 翻車魚; fān chē yú, meaning "toppled wheel fish". Many of the sunfish's various names allude to its flattened shape.
French polymath Guillaume Rondelet wrote about the ocean sunfish in his 1554 work de Piscibus, using the term Orthagoriscus, "sucking pig" for the likeness of its body and mouth. It was originally classified in the pufferfish family as Tetraodon mola, its epithet mola is Latin for "millstone", which the fish resembles because of its gray color, rough texture, and rounded body. It is now placed in its own genus Mola and family name Molidae as the type species with two other species: Mola tecta and M. alexandrini (previously known as Mola ramsayi). Extinct relatives of Mola mola lived in the Oligocene and Miocene epochs. However, the earliest known fossil remains of Mola mola itself were found in archaeological middens dating to the Holocene epoch.

The common name "sunfish" without qualifier is used to describe the marine family Molidae and the freshwater sunfish in the family Centrarchidae, which is unrelated to Molidae. On the other hand, the name "ocean sunfish" and "mola" refer only to the family Molidae.

It shares many traits common to members in the order Tetraodontiformes including pufferfish, porcupinefish, and filefish like having a beak formed from four fused teeth; sunfish fry resemble spiky pufferfish more than they resemble adult molas.

The caudal fin of the ocean sunfish is replaced by a rounded clavus, creating the body's distinct truncated shape. The body is flattened laterally, giving it a long oval shape when seen head-on. The pectoral fins are small and fan-shaped, while the dorsal fin and the anal fin are lengthened, often making the fish as tall as it is long. Specimens up to 3.3 m (10 ft 10 in) in height have been recorded.

The mature ocean sunfish has an average length of 1.8 m (5 ft 11 in) and a fin-to-fin length of 2.5 m (8 ft 2 in) . The weight of mature specimens can range from 247 to 1,000 kg (545 to 2,205 lb), but even larger individuals are not unheard of . The maximum size recorded is 3.3 m (10 ft 10 in) in length, and maximum weight recorded is 2,300 kg (5,100 lb).

The spinal column of M. mola contains fewer vertebrae and is shorter in relation to the body than that of any other fish. Although the sunfish descended from bony ancestors, its skeleton contains largely cartilaginous tissues, which are lighter than bone, allowing it to grow to sizes impractical for other bony fishes. Its teeth are fused into a beak-like structure, which prevents them from being able to fully close their mouths, while also having pharyngeal teeth located in the throat.

The sunfish lacks a swim bladder. Some sources indicate the internal organs contain a concentrated neurotoxin, tetrodotoxin, like the organs of other poisonous tetraodontiformes, while others dispute this claim.
In the course of its evolution, the caudal fin (tail) of the sunfish disappeared, to be replaced by a lumpy pseudotail, the clavus. This structure is formed by the convergence of the dorsal and anal fins, and is used by the fish as a rudder. The smooth-denticled clavus retains 11–14 fin rays and terminates in a number of rounded ossicles.

Ocean sunfish often swim near the surface, and their protruding dorsal fins are sometimes mistaken for those of sharks. However, the two can be distinguished by the motion of the fin. Unlike most fish, the sunfish swings its dorsal fin and anal fin in a characteristic sculling motion.
Adult sunfish range from brown to silvery-grey or white, with a variety of region-specific mottled skin patterns. Coloration is often darker on the dorsal surface, fading to a lighter shade ventrally as a form of countershading camouflage. M. mola also exhibits the ability to vary skin coloration from light to dark, es…

Read more on Wikipedia

Ocean sunfish are native to the temperate and tropical waters of every ocean in the world. Mola genotypes appear to vary widely between the Atlantic and Pacific, but genetic differences between individuals in the Northern and Southern hemispheres are minimal.

Although early research suggested sunfish moved around mainly by drifting with ocean currents (which has resulted in the sunfish sometimes being characterized as a megaplankton ), individuals have been recorded swimming 26 km (16 mi) in a day at a cruising speed of 3.2 km/h (1.7 kn). They are also capable of moving rapidly when feeding or avoiding predators, to the extent that they can vertically leap out of water. Contrary to the perception that the fish spend much of their time basking at the surface, M. mola adults actually spend a large portion of their lives actively hunting at depths greater than 200 m (660 ft), occupying both the epipelagic and mesopelagic zones. Sunfish are most often found in water warmer than 10 °C (50 °F); prolonged periods spent in water at temperatures of 12 °C (54 °F) or lower can lead to disorientation and eventual death. Surface basking behavior, in which a sunfish swims on its side, presenting its largest profile to the sun, may be a method of "thermally recharging" following dives into deeper, colder water in order to feed. Sightings of the fish in colder waters outside of its usual habitat, such as those southwest of England, may be evidence of increasing marine temperatures.

Sunfish are usually found alone, but occasionally in pairs.