The pursuit of fractionalized particles outside the extreme conditions of a quantizing magnetic field has been a longstanding quest of solid state physics. Recent experiments have reported fractional quantized anomalous hall states — the analogue of fractional quantum hall (FQAH) states but at zero magnetic field — in twisted bilayers of MoTe2 and rhombohedral graphene systems. When should we expect such unusual topological phases, and what new phenomena should they have? To answer these questions I first introduce the framework of “vortexable” or “ideal” Chern bands. Vortexable bands have a fixed operator that introduces a vortex into any band wave function while keeping the state entirely within the same band, just as in the lowest Landau level. Such bands admit trial wave functions for FQAH states, akin to Laughlin states, that are exact many-body ground states for short-ranged interactions in the absence of dispersion. Nearly-vortexable bands appear in twisted MoTe2, explaining their fractionalized physics. I will present many body calculations showing tMoTe2 should admit a broad composite Fermi liquid phase (a non-Fermi liquid) centered around 3.6°. I will then shift to the stranger case of rhombohedral graphene whose fractional phases may be due to an anomalous Hall crystal, a topological analogue of a Wigner crystal. Finally, I will present an optical signature involving “extinguished” circular dichroism as a means to identify nearly-vortexable Chern bands.