Colloidal suspensions exhibit fascinating phase behaviors due to the subtle bal- ance between hydrodynamic and Brownian diffusion at low shear rate. While the phase transitions in the equilibrium / near-equilibrium suspensions have been stud- ied extensively, not much is known for the phase dynamics of suspensions in the hydrodynamic limit. In this talk, I will review some of our recent findings on the phase transitions of non-Brownian suspensions. The phase dynamics are studied by using a multiscale force-coupling method, which can simultaneously account for both near-field lubrication and far-field multi-body hydrodynamic interactions. When a basic inhomogeneity is introduced into the system by confining walls, the suspensions may undergo very interesting phase transitions, depending on the volume fraction, distance from the wall and size of the gap. Due to the phase transitions, suspensions of sedimenting particles may exhibit hysteresis and bifurcation. It is shown that the phase transitions of the confined, non-Brownian suspensions can be manipulated by applying external couple on the suspended particles, which alters the bulk mechan- ical properties of the mixture. Finally, phase behaviors of bi-disperse suspensions of spherical rotors will be discussed. At low volume fractions, the counter-rotating rotors tend to stay together, which changes to clusters of co-rotating rotors at high volume fractions. Eventually, above a critical volume fraction, crystal structures of counter-rotating rotors emerge, which accompanies a sharp drop in the energy conversion rate from the rotational to the translational kinetic energies.