An overview of the severe plastic deformation (SPD) of high entropy alloys (HEAs) is given with a focus on microstructure and texture evolution, phase transformation, strength and ductility, superplasticity, and thermal stability. It combines the now well-established research area of SPD with that of a recently discovered new class of advanced materials. The peculiarities of HEAs in relation to SPD are shown, such as phase decomposition and reduced grain growth. This offers the possibility of producing ultra-hard HEA materials by SPD processes or by post-annealing and enables extremely high superplasticity at high strain rates. The effect of SPD on changing properties is demonstrated mainly for the prototypes fcc Cantor and bcc Senkov HEA, but few examples of more complex HEAs indicate the high research potential of these advanced materials in the field of nanoSPD.