The experimental discovery of fractional Chern insulators (FCIs) in moiré materials marks a significant development in the study of highly entangled quantum materials. FCIs differ from the traditional fractional quantum Hall effect not only because they occur without external magnetic fields but also because of essential lattice effects that give rise to topologically non-trivial moiré bands. Despite these differences, the sequence of FCIs observed in moiré transition metal dichalcogenides and multi-layer graphene aligns with the hierarchy of Jain states found in the conventional FQH system, which can be interpreted in terms of composite fermions. Motivated by these experimental results, in this talk, we will present an analysis of composite fermions that provides a roadmap to understanding Abelian FCIs in twisted bilayer MoTe2. The interplay between the moiré periodic potentials and the Chern-Simons gauge field gives rise to a fractal Hofstadter spectrum of composite fermions characterized a complex structure of incompressible states and topological bands. Among these, we identify both FCIs consistent with the Jain hierarchy and new classes of FCIs whose transport properties differ from those of the Jain sequence. We also discuss the influence of the displacement field, suppressing composite fermion gaps and inducing topological phase transitions.