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In the second part of the talk, I will describe the effects of a superlattice on the nature of the fractional quantum Hall effect. Recent theoretical work, largely motivated by efforts to engineer fractional quantum Hall states in optical lattice systems, has suggested that new kinds of fractional quantum Hall states--termed fractional Chern insulators--can exist in lattice systems with intrinsically finite bandwidth. At high magnetic field in our devices, a substrate-induced moire superlattice gives rise to a variety of Hofstadter bands with different Chern numbers. We find a wide variety of incompressible states at fractional filling of these bands characterized by fractionally quantized Hall conductance. These results demonstrate that fractional Chern insulators are indeed a generic phenomenon. Going forward, we anticipate being able to place approximate limits on the required interaction strength and bandwidth required to realize these phases.