Mitochondria are recognized as the main source of ATP to meet the energy demands of the cell. ATP production occurs by oxidative phosphorylation when electrons are transported through the electron transport chain (ETC) complexes and develop the proton motive force across the inner mitochondrial membrane that is used for ATP synthesis. Studies since the 1960s have been concentrated on the two models of structural organization of ETC complexes known as "solid-state" and "fluid-state" models. However, advanced new techniques such as blue-native gel electrophoresis, mass spectroscopy, and cryogenic electron microscopy for analysis of macromolecular protein complexes provided new data in favor of the solid-state model. According to this model, individual ETC complexes are assembled into macromolecular structures known as respiratory supercomplexes (SCs). A large number of studies over the last 20 years proposed the potential role of SCs to facilitate substrate channeling, maintain the integrity of individual ETC complexes, reduce electron leakage and production of reactive oxygen species, and prevent excessive and random aggregation of proteins in the inner mitochondrial membrane. However, many other studies have challenged the proposed functional role of SCs. Recently, a third model known as the "plasticity" model was proposed that partly reconciles both "solid-state" and "fluid-state" models. According to the "plasticity" model, respiratory SCs can co-exist with the individual ETC complexes. To date, the physiological role of SCs remains unknown, although several studies using tissue samples of patients or animal/cell models of human diseases revealed an associative link between functional changes and the disintegration of SC assembly. This review summarizes and discusses previous studies on the mechanisms and regulation of SC assembly under physiological and pathological conditions.