Interaction of atomic and molecular particles with dielectric surfaces has been attracting considerable attention over the past years, in order to understand various fundamental problems important in catalysis, development of gas sensors, problems of adhesion etc. Detailed quantitative information about the dynamics of electron transfer, which plays an important role in chemisorption and reactions at surfaces, has been recently obtained from experiments in which ionic or atomic beams are scattered off dielectric surfaces and the charge states of particles are analysed, providing in particular site-specific information on electron transfer. These experiments have shown that the dynamics of electron transfer on semiconductor and insulator surfaces cannot be understood within simple models extensively used for the case of metal surfaces. It was shown in particular that in spite of the existence of large bandgaps and at first sight the unfavourable situation for resonant electron transfer, negative ion formation occurs quite efficiently. Together with the existence of an efficient electron capture process associated with negative ion formation the existence of electron loss processes was demonstrated by use of both atoms and negative ions as projectiles. Various theoretical descriptions for describing electron capture and loss phenomena have been developed. In this review the experimental approaches and results are outlined along with the theoretical concepts and approaches developed to treat electron transfer phenomena on dielectric surfaces.