Compact binary systems in which a white dwarf (WD) accretes material from a non-degenerate companion, constitute some of the most prevalent, yet intriguing astronomical objects in the universe. Of special interest is a class of these binaries known as cataclysmic variables (CVs), where the transfer of material from a red dwarf companion to the WD instigates a wide range of energetic processes causing transient, variable and eruptive behaviour. These binaries, as well as a closely related class of objects known as supersoft X-ray sources (SSSs) are therefore fascinating cosmic laboratories in which the effects of fundamentally important physical phenomena like turbulence, magnetic fields, gravitation, viscosity, and particle acceleration can be studied, by modelling the observed electromagnetic radiation, from the low energy radio waves all the way up to gamma-ray energies. Several CVs and SSSs have been shown to exhibit high-velocity outflows, many of which are expected to be driven by magnetic fields, and modern instruments have recently shown that these outflows are associated with radio and gamma-ray emission. These developments open up an exciting new area in this field. The upcoming commissioning of MeerKAT, as well as the newly available spectropolarimetric mode on SALT, in combination with international high-energy facilities, makes this the ideal time to undertake studies of the non-thermal emission in CVs in the form of synchrotron radio emission, and non-thermal optical emission, as well as potential particle acceleration yielding high energy emission.