  Irreversibility is a fundamental concept with important implications at many
levels. It pinpoints the fundamental difference between the intrinsically
reversible microscopic equations of motion and the unidirectional arrow of time
that emerges at the macroscopic level. More pragmatically, a full
quantification of the degree of irreversibility of a given process can help in
the characterisation of the performance of thermo-machines operating at the
quantum level. Here, we review the concept of entropy production, which is
commonly intended as {\it the} measure of thermodynamic irreversibility of a
process, pinpointing the features and shortcomings of its current formulation.
