This tutorial review is intended to provide an accessible and self-contained introduction to the discipline of electromagnetic scattering by nonspherical particles and discuss the most general ways in which the scattering and absorption properties of particles and small random particle groups are affected by particle morphology. The main focus is on how nonsphericity influences our way of describing and quantifying electromagnetic scattering by particles and how it is likely to affect, both qualitatively and quantitatively, the principal theoretical descriptors of scattering and the relevant optical observables. Several quantitative examples included in this review are the result of a controlled laboratory measurement or a numerically exact theoretical computation and are intended to illustrate the main theses and conclusions.