We present an overview of the current interest in non-collinear magnetism in multiferroic perovskite crystals. We first describe the different microscopic mechanisms giving rise to the non-collinearity of spins in this class of materials. We discuss, in particular, the interplay between non-collinear magnetism and ferroelectric and antiferrodistortive distortions of the perovskite structure, and how this can promote magnetoelectric responses. We then provide a literature survey on non-collinear multiferroic perovskites. We discuss numerous examples of spin cantings driving weak ferromagnetism in transition metal perovskites, and of spin-induced ferroelectricity as observed in the rare-earth based perovskites. These examples are chosen to best illustrate the fundamental role of non-collinear magnetism in the design of multiferroicity.