In this paper, we discuss the application of IsoGeometric Analysis to incompressible viscous flow problems. We consider, as a prototype problem, the Stokes system and we propose various choices of compatible spline spaces for the approximations to the velocity and the pressure fields. The proposed choices can be viewed as extensions of the Taylor–Hood, Nédélec and Raviart–Thomas pairs of finite element spaces, respectively. We study the stability and convergence properties of each method and discuss the conservation properties of the discrete velocity field in each case. Copyright © 2010 John Wiley & Sons, Ltd.