  Entropy production is a key quantity in any finite-time thermodynamic
process. It is intimately tied with the fundamental laws of thermodynamics,
embodying a tool to extend thermodynamic considerations all the way to
non-equilibrium processes. It is also often used in attempts to provide the
quantitative characterization of logical and thermodynamic irreversibility,
stemming from processes in physics, chemistry and biology. Notwithstanding its
fundamental character, a unifying theory of entropy production valid for
general processes, both classical and quantum, has not yet been formulated.
Developments pivoting around the frameworks of stochastic thermodynamics, open
quantum systems, and quantum information theory have led to substantial
progress in such endeavour. This has culminated in the unlocking of a new
generation of experiments able to address stochastic thermodynamic processes
and the impact of entropy production on them. This paper aims to provide a
compendium on the current framework for the description, assessment and
manipulation of entropy production. We present both formal aspects of its
formulation and the implications stemming from the potential quantum nature of
a given process, including a detailed survey of recent experiments.
