The study of combinatorial properties of finite point configurations is a vast area of research in geometry, whose origins go back at least to the ancient Greeks. Since it includes virtually all problems starting with “consider a set of n points in space,” space limitations impose the necessity of making choices. As a result, we will restrict our attention to Euclidean spaces and will discuss problems that we find particularly important. The chapter is partitioned into incidence problems (Section 1.1), metric problems (Section 1.2), and coloring problems (Section 1.3).