The partial-intensity approach for simulating electron scattering is outlined, and relevant algorithms that were introduced in the past decade are presented. This is important for understanding the signal generation and surface sensitivity for a wide variety of techniques such as X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), Auger-photoelectron coincidence spectroscopy (APECS), elastic peak electron spectroscopy (EPES), reflection electron energy loss spectroscopy (REELS), electron probe microanalysis (EPMA), total electron yield (TEY) and the like. In particular, the so-called trajectory-reversal algorithm is discussed, both for emission problems (relevant for XPS, AES, and APECS) as well as for reflection problems (relevant for EPES and REELS), as this algorithm allows one to achieve enhanced efficiencies in simulations of many orders of magnitude compared to a conventional simulation. It is then shown that the simulation of the partial intensities (i.e. the number of n-fold inelastically scattered electrons) is not only useful for simulation of model spectra but is also essential for truly quantitative interpretation of experimental spectra. Finally, the stochastic process for multiple scattering beyond the constant cross-section approximation is treated. Using the generalized stochastic process, the above approaches can be extended to techniques such as EPMA, TEY and the like in a straightforward way. Illustrative examples are given for the topics mentioned above.