The cytochrome bc₁ complex (bc₁) is the mid-segment of the cellular respiratory chain of mitochondria and many aerobic prokaryotic organisms; it is also part of the photosynthetic apparatus of non-oxygenic purple bacteria. The bc₁ complex catalyzes the reaction of transferring electrons from the low potential substrate ubiquinol to high potential cytochrome c. Concomitantly, bc₁ translocates protons across the membrane, contributing to the proton-motive force essential for a variety of cellular activities such as ATP synthesis. Structural investigations of bc₁ have been exceedingly successful, yielding atomic resolution structures of bc₁ from various organisms and trapped in different reaction intermediates. These structures have confirmed and unified results of decades of experiments and have contributed to our understanding of the mechanism of bc₁ functions as well as its inactivation by respiratory inhibitors. This article is part of a Special Issue entitled: Respiratory complex III and related bc complexes.