We describe some preconditioning approaches for the two-by-two block matrices as arising in discrete models of the Navier-Stokes problem in its various forms (constant or variable coefficients, stationary or time-dependent). We assume that the discretization is done using proper finite element discretisation - either using stable finite element pairs or it has been properly stabilized. We consider the Navier-Stokes equations in their full complexity, including time-dependence and variable density. The original system of partial differential equations includes the Navier-Stokes equations and one more equation for the density, which varies in time and space. We discuss some popular splitting schemes for this problem, their pros and cons. A reformulation of the problem is described, where instead of the velocity, one can use the so-called momentum.