Abstract: In this talk, I try to analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices. Conditions under which the FQH effect can be achieved for bosons on a lattice with an effective magnetic field and finite onsite interaction, will be investigated. Furthermore, we characterize the ground state in such systems by calculating Chern numbers which can provide direct signatures of topological order and explore regimes where the characterization in terms of wavefunction overlap fails. We also discuss various issues which are relevant for the practical realization of such FQH states with ultra cold atoms in an optical lattice, including the presence of the long-range dipole interaction which can improve the energy gap and stabilize the ground state. We also investigate a new detection technique based on Bragg spectroscopy to probe these system in an experimental realization.