We present a framework to compute and study two-dimensional gravity-capillary water waves that are quasi-periodic in space. This means they can be represented as periodic functions on a higher-dimensional torus by evaluating along irrational directions. We consider both traveling waves and the general initial value problem. In both cases, the nonlocal Dirichlet-Neumann operator is computed using conformal mapping methods and a quasi-periodic variant of the Hilbert transform. For traveling waves, we consider continuation paths that begin either as perturbations of the flat rest state (a generalization of the Wilton ripple problem) or as interior bifurcations from larger-amplitude periodic traveling waves. For the time-dependent problem, we give an example of a periodic wave profile that is set in motion with a quasi-periodic velocity potential. This causes some of the wave crests to overturn while others flatten out -- no two crests evolve in exactly the same way. If time permits, I will also briefly discuss a new shooting method to compute temporally quasi-periodic water waves.