The family Molidae (ocean sunfishes, molids) is within the order Tetraodontiformes and includes the world’s heaviest bony fish, certified in the Guinness World Records. Fishes in the Molidae family lack a caudal fin, and instead have a unique posterior structure called a clavus. The huge body size and strange shape of most of this family’s members have long fascinated researchers. Through the years, the scientific names of Molidae grew to 56 nominal species, and its classification was confused. At present, however, three genera and five species are recognized: Ranzania laevis (Pennant 1776), Masturus lanceolatus (Liénard 1840), Mola tecta Nyegaard et al. 2017, Mola alexandrini (Ranzani 1839) and Mola mola (Linnaeus 1758). Since their initial descriptions more than 500 years ago, various species of molid, particularly within the genus Mola, have been misidentified due to similarities in external shape. The advent of molecular phylogenetic studies has brought greater taxonomic clarity to the group. This chapter focuses on the history and classification of the five currently recognized species of Molidae. A key defining the characteristics of each member of the Molidae family is provided. The chapter also reviews the various external molid forms, the derivation of their scientific names, maximum weight and length records, range and habitats and lastly, highlights remaining questions.