  Data from the Van Allen Probes have provided the first extensive evidence of
non-linear (as opposed to quasi-linear) wave-particle interactions in space
with the associated rapid (fraction of a bounce period) electron acceleration
to hundreds of keV by Landau resonance in the parallel electric fields of time
domain structures (TDS) and very oblique chorus waves. The experimental
evidence, simulations, and theories of these processes are discussed. {\bf Key
words:} the radiation belts, wave-particle interaction, plasma waves and
instabilities
