Algebraic geometry is to a large extent concerned with classifying algebraic zero-sets with given properties. A Hilbert scheme is the set of all zero sets with specific numeric invariants. It happens that this set is the zero set of a system of polynomials too! Grothendieck first defined and proved some of the basic properties of Hilbert schemes. In this talk, we give an elementary and explicit view of Hilbert schemes. A Groebner basis gives rise to a path on a Hilbert scheme. This structure allows us to study Hilbert schemes from a combinatorial point of view, giving a “roadmap” of a Hilbert scheme (more like a map of metro stations!). We describe this structure, as well as some open problems in this area. We assume no knowledge of Groebner bases or algebraic geometry.