Abstract: In this tutorial review paper, we illustrate how computer modeling can contribute to a better insight in inductively coupled plasma-mass spectrometry (ICP-MS). We start with a brief overview on previous efforts, studying the fundamentals of the ICP and ICP-MS, with main focus on previous modeling activities. Subsequently, we explain in detail the model that we developed in previous years, and we show typical calculation results, illustrating the plasma characteristics, gas flow patterns and the sample transport, evaporation and ionization. We also present the effect of various experimental parameters, such as operating conditions, geometrical aspects and sample characteristics, to illustrate how modeling can help to elucidate the optimal conditions for improved analytical performance.