Nonnegative matrices arise naturally in a number of models of physical and biological phenomena. The reason for this is transparent: many of the quantities that come up in those settings are necessarily nonnegative. In this chapter, we present two examples of nonnegative matrices; one arises in mathematical demography, the other in stochastic processes. In both instances, we indicate how the group inverse of an appropriate M-matrix can be used to analyse the model. Our aim is to help motivate the kinds of questions raised in later chapters, and to give the reader a sense of the techniques upon which we will focus.