Descriptive combinatorics is an exciting recently emerged area that combines ideas from such diverse fields as graph theory, set theory, analysis, dynamical systems, and computer science. Roughly speaking, descriptive combinatorics investigates classical combinatorial problems (e.g., colorings, matchings, etc.) on infinite graphs that are equipped with some extra structure such as a topology or a measure. This extra structure precludes the use of many natural proof techniques that are available in finite graph theory. For example, the first step in many graph-theoretic constructions is to pick a vertex in each connected component of the given graph. This causes no issues in the finite case, but if we are working with an infinite graph, then picking a vertex in each component requires the use of the Axiom of Choice---a notoriously non-constructive fact that easily leads to highly "pathological" results. But what if a choice of a vertex in every component is already given to us? Can we avoid "pathologies" then? In this talk I will discuss this question and along the way provide an introduction to some of the basic ideas in descriptive combinatorics.