These notes give an overview of recent results concerning the non-linear stochastic wave equation in spatial dimensions d >= 1, in the case where the driving noise is Gaussian, spatially homogeneous and white in time. We mainly address issues of existence, uniqueness and Holder-Sobolev regularity. We also present an extension of Walsh's theory of stochastic integration with respect to martingale measures that is useful for spatial dimensions d >= 3.