Abstract: In the first part of my talk I will discuss the physics of two and three ultracold Rydberg atoms interacting via the dipole-dipole interaction. These systems can form micrometer sized dimer molecules whose relative dynamics is governed by artificial gauge fields. In particular I will show that these fields exhibit magnetic monopoles and give rise to synthetic spin-orbit coupling. Furthermore, I will discuss three atom bound states that do not have a two atom equivalent.  The binding mechanism leading to these states is substantially different from Efimov physics. I will also show how these molecular states can be engineered in the laboratory and how the exaggerated properties of Rydberg atoms make their features directly observable using current experimental technology. In the second part of my talk I will discuss the prospect of forming strongly correlated electron gases starting from ultracold Rydberg atoms in optical lattices. I will describe our progress in electronic structure calculations for Rydberg atoms with electrons that are delocalized over the optical lattice. I will explain how this system might form a Rydberg crystal with strongly correlated electrons, a spatial periodicity of several hundred nanometers, and coherent dynamics on experimentally resolvable picosecond time scales. I will present the exciting properties that such an electronic system might possess and discuss some of the major challenges in realizing them.