We investigate the cubic stochastic nonlinear wave equation (SNLW) on the two-dimensional torus, driven by spatial noise rougher than white noise. The problem is how rough can we take the noise for there is a well-posed solution theory. The solution would be the of the form of the sum of a rough term, obtained by solving a linear stochastic equation, and a smooth part. We report the progress so far. This is joint work with Xianfeng Ren.