In the first part of the talk, I will discuss the formation of a BEC of excitons in bilayer 2D electron systems. The lack of agreement between mean field predictions and experimental observations motivated us to develop a 2D non-perturbative bosonization approach to study the problem [1]. A generalization of the formalism to the SU(4) case is appropriate for describing the quantum Hall effect in graphene [2]. In the second part of the talk, I will discuss an experimental set-up recently proposed by us [3], which may allow for the realization of a staggered-flux phase in a 2D optical lattice loaded with bosons. The effective Hamiltonian of the system is a Bose-Hubbard one, with complex and anisotropic hopping coefficients. A very rich phase diagram emerges from the model: besides the usual Mott-insulator and zero-momentum condensate, a new phase with a finite momentum condensate becomes the ground-state at high-rotation [4]. This staggered-flux phase bears analogies with the d-density wave discussed in the context of high-Tc superconductors, and also with the Fulde-Ferrel-Larkin-Ovchinnikov phase.