Solar hard X-ray emission is one of the most direct diagnostics of accelerated particles during solar flares. In this review, the current understanding of hard X-ray emission processes is discussed: first the different emission mechanisms (in particular inverse Compton radiation, energetic ion or electron bremsstrahlung) are presented and the plausibility of each of these mechanisms is discussed. Then, different types of hard X-ray models (thermal or non-thermal, homogeneous or inhomogeneous emission regions) are presented together with the comparison of their predictions with X-ray observations (spectral, spatial and temporal informations -directivity and polarization).