  We review the recent theoretical developments towards understanding the Mott
phases and quantum phase transition of extended Bose-Hubbard models on lattices
in two spatial dimensions . We focuss on the description of these systems using
the dual vortex picture and point out the crucial role played by the geometry
of underlying lattices in determining the nature of both the Mott phases and
the quantum phase transitions. We also briefly compare the results of dual
vortex theory with quantum Monte Carlo results.
