Fractional Chern insulators or fractional quantum anomalous Hall (FQAH) states were proposed theoretically more than a decade ago. These exotic states of matter are fractional quantum Hall states realized when a nearly flat Chern band is partially filled, even in the absence of an external magnetic field. Exciting experimental signatures of such states have recently been reported in MoTe$_2$ and graphene moiré superlattices. In the fractional quantum Hall (FQH) context, Jain's composite fermion construction based on the flux attachment intuition has been demonstrated to be very successful in understanding a large class of FQH states in Landau levels. However, how to microscopically perform flux attachment and understand the FQAH states is not known. Motivated by these experimental and theoretical issues, I will talk about a projective construction for the composite fermion states in a partially filled Chern band, which can capture the microscopics, e.g., symmetry fractionalization patterns, composite fermion and magnetoroton band structures. On the mean-field level, the ground states' and excited states' composite fermion wavefunctions are found self-consistently in an enlarged Hilbert space. Beyond the mean field, these wavefunctions can be projected back to the physical Hilbert space to construct the electronic wavefunctions, allowing direct comparison with FCI states from exact diagonalization on finite lattices. We find that the projected electronic wavefunction corresponds to the combinatorial hyperdeterminant of a tensor. When applied to the traditional Galilean invariant Landau level systems, the present construction reproduces Jain's composite fermion wavefunctions exactly. Future directions and open questions will be discussed.