Pulsed electron beams allow for the direct atomic-scale observation of structures with femtosecond to picosecond temporal resolution in a variety of fields ranging from materials science to chemistry and biology, and from the condensed phase to the gas phase. Motivated by recent developments in ultrafast electron diffraction and imaging techniques, we present here a comprehensive account of the fundamental processes involved in electron pulse propagation, and make comparisons with experimental results. The electron pulse, as an ensemble of charged particles, travels under the influence of the space–charge effect and the spread of the momenta among its electrons. The shape and size, as well as the trajectories of the individual electrons, may be altered. The resulting implications on the spatiotemporal resolution capabilities are discussed both for the N-electron pulse and for single-electron coherent packets introduced for microscopy without space–charge.