We often encounter sequences of representations of a family of groups. For example, the cohomology of ordered configurations of n distinct points on a manifold is a representation of the symmetric group Sn. Similarly, the homology of the congruence subgroup of level m inside GLn(Z) is a representation of GLn(Z/mZ). As n grows to infinity the two examples above become, in a sense, stable as representations. Stable representations can be thought of as finitely generated objects in a suitable functor category. This point of view is due to Church-Ellenberg-Farb who introduced and studied such a category called FI-modules. We provide an introduction to FI-modules and explain what it entails about the examples above.