  X-radiation from energetic electrons is the prime diagnostic of
flare-accelerated electrons. The observed X-ray flux (and polarization state)
is fundamentally a convolution of the cross-section for the hard X-ray emission
process(es) in question with the electron distribution function, which is in
turn a function of energy, direction, spatial location and time. To address the
problems of particle propagation and acceleration one needs to infer as much
information as possible on this electron distribution function, through a
deconvolution of this fundamental relationship. This review presents recent
progress toward this goal using spectroscopic, imaging and polarization
measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch
angle) and spatial distributions of energetic electrons in solar flares are
critically reviewed. We discuss the role and the observational evidence of
several radiation processes: free-free electron-ion, free-free
electron-electron, free-bound electron-ion bremsstrahlung, photoelectric
absorption and Compton back-scatter (albedo), using both spectroscopic and
imaging techniques. This unprecedented quality of data allows for the first
time inference of the angular distributions of the X-ray-emitting electrons
using albedo, improved model-independent inference of electron energy spectra
and emission measures of thermal plasma. Moreover, imaging spectroscopy has
revealed hitherto unknown details of solar flare morphology and detailed
spectroscopy of coronal, footpoint and extended sources in flaring regions.
Additional attempts to measure hard X-ray polarization were not sufficient to
put constraints on the degree of anisotropy of electrons, but point to the
importance of obtaining good quality polarization data.
