  We review the recent progress in understanding the properties of spin-split
superconductors under non-equilibrium conditions. Recent experiments and
theories demonstrate a rich variety of transport phenomena occurring in devices
based on such materials that suggest direct applications in thermoelectricity,
low-dissipative spintronics, radiation detection and sensing. We discuss
different experimental situations and present a theoretical framework based on
quantum kinetic equations. Within this framework we provide an accurate
description of the non-equilibrium distribution of charge, spin and energy,
which are the relevant non-equilibrium modes, in different hybrid structures.
We also review experiments on spin-split superconductors and show how transport
measurements reveal the properties of the non-equilibrium modes and their
mutual coupling. We discuss in detail spin injection and diffusion and very
large thermoelectric effects in spin-split superconductors.
