The importance of interpretation of hard X-ray burst spectra, polarisation and directivity to the flare process as a whole is emphasised. After critically reviewing observations of these and related burst characteristics, the problems of analytic and numerical inversion of the X-ray spectrum to give the flare electron spectrum are discussed and it is concluded that electron spectra cannot be accurately and unambiguously inferred from their bremsstrahlung emission. Consideration of directional, albedo, and model-dependent effects, on the other hand, shows that none of the X-ray data are at present inconsistent with a power-law electron acceleration spectrum.
Characteristics of thick-target, thin-target and electron-trap models of hard X-ray sources are discussed quantitatively and their ability to fit the observations is examined. Selection of a satisfactory model is precluded by lack of both sufficient observations and of adequate theoretical description of models. Nevertheless, it is suggested that redistribution of the flaring atmosphere and the effects of collective energy losses may reconcile even behind-the-limb burst observations and interplanetary electron spectra with a thick-target description (which fits other data well). This is attractive since a thick-target X-ray source makes the minimal demand on flare energy. Even a thick-target, however, requires an embarrassingly large number and energy of fast electrons. Therefore the review is completed by discussing how these requirements might be reduced if thermal emission extended to hard X-ray energies or if multiple reacceleration of electrons occurred.