Layered moire systems have become an outstandingly versatile platform for the study of strongly correlated quantum phenomena, due to the possibility to tune the band structure to obtain a flat band. Topological properties are also expected in many moire systems: for example, aligning magic angle twisted bilayer graphene with a substrate of hexagonal boron nitride (hBN) creates flat valence and conduction bands with Chern number +/- 1. A nearly flat Chern band can host an analog of the fractional quantum Hall effect in the absence of a magnetic field, a fractional Chern insulator. I will discuss which microscopic ingredients are necessary for this phase to arise, and show that these conditions may be found in magic angle twisted bilayer graphene aligned with hBN. Based on the results of exact diagonalization, I will show that both a spin singlet and spin polarized fractional Chern insulators are possible depending on the fine details of the band properties of this material, and discuss how this theoretical analysis applies to recent experimental results. Online Seminar