The present review is an attempt to conceptualize a contemporary understanding about the roles that cardiolipin, a mitochondrial specific conical phospholipid, and non-bilayer structures, predominantly found in the inner mitochondrial membrane (IMM), play in mitochondrial bioenergetics. This review outlines the link between changes in mitochondrial cardiolipin concentration and changes in mitochondrial bioenergetics, including changes in the IMM curvature and surface area, cristae density and architecture, efficiency of electron transport chain (ETC), interaction of ETC proteins, oligomerization of respiratory complexes, and mitochondrial ATP production. A relationship between cardiolipin decline in IMM and mitochondrial dysfunction leading to various diseases, including cardiovascular diseases, is thoroughly presented. Particular attention is paid to the targeting of cardiolipin by Szeto–Schiller tetrapeptides, which leads to rejuvenation of important mitochondrial activities in dysfunctional and aging mitochondria. The role of cardiolipin in triggering non-bilayer structures and the functional roles of non-bilayer structures in energy-converting membranes are reviewed. The latest studies on non-bilayer structures induced by cobra venom peptides are examined in model and mitochondrial membranes, including studies on how non-bilayer structures modulate mitochondrial activities. A mechanism by which non-bilayer compartments are formed in the apex of cristae and by which non-bilayer compartments facilitate ATP synthase dimerization and ATP production is also presented.