Fractional Chern Insulators (FCIs) are lattice systems that realize the fractional quantum Hall effect without an external magnetic field. They have been theoretically discovered a few years ago in exact diagonalization studies and a lot of what is known about these systems relies on numerical methods. In this talk I will present a theoretical framework aimed at understanding the topological properties of FCIs. This approach is based on a Chern-Simons composite fermion theory for FCIs, whereby bare fermions are mapped into composite fermions coupled to a lattice Chern-Simons gauge theory. I will apply this construction to a Chern insulator model on the kagome lattice and identify a rich structure of gapped topological phases characterized by fractionalized excitations including states with unequal filling and Hall conductance. Gapped states with the same Hall conductance at different filling fractions are characterized as realizing distinct symmetry fractionalization classes. This work is a collaboration with Ramanjit Sohal and Eduardo Fradkin (arXiv: 1707.06118).