Major progress has been made in defining the basis of the mitochondrial permeability transition, a Ca2+‐dependent permeability increase of the inner membrane that has puzzled mitochondrial research for almost 70 years. Initially considered an artefact of limited biological interest by most, over the years the permeability transition has raised to the status of regulator of mitochondrial ion homeostasis and of druggable effector mechanism of cell death. The permeability transition is mediated by opening of channel(s) modulated by matrix cyclophilin D, the permeability transition pore(s) (PTP). The field has received new impulse (a) from the hypothesis that the PTP may originate from a Ca2+‐dependent conformational change of F‐ATP synthase and (b) from the reevaluation of the long‐standing hypothesis that it originates from the adenine nucleotide translocator (ANT). Here, we provide a synthetic account of the structure of ANT and F‐ATP synthase to discuss potential and controversial mechanisms through which they may form high‐conductance channels; and review some intriguing findings from the wealth of early studies of PTP modulation that still await an explanation. We hope that this review will stimulate new experiments addressing the many outstanding problems, and thus contribute to the eventual solution of the puzzle of the permeability transition. The mechanistic basis for the mitochondrial permeability transition (an inner membrane permeability increase that is a causative event in cell death) has puzzled mitochondrial research for 70 years. Here, we review the field and discuss recent evidence on how a Ca2+‐dependent conformational change of F‐ATP synthase and of adenine nucleotide translocator may transform these energy‐conserving devices into energy‐dissipating multiconductance channels causing the permeability transition.