Both in biological and synthetic lipid membranes, lateral lipid organizations into domains and membrane curvatures are ubiquitous features. In this talk, I will discuss how the interplay between phase separation and curvature can give rise to interesting cooperative behaviours. In the first part of the talk, I will describe our recent work on bicontinuous cubic membranes, whereby the lipids form a triply periodic lipid bilayer that separates two percolating and non-intersecting water channels. Upon considering interaction between different species we find an interesting competition between a curvature favoured splitting and an interfacially favoured coalescing mechanism of single species domains. With increasing the line tension contribution, we also observe a facetting of the domains that we explain with a simple argument based on the symmetry of the underlying surface and topology. In the second part of the talk, I will discuss a simple colloidal model motivated by protein distributions on the membranes of purple bacteria, where we focus only on non-specific interactions. Our results suggest that phase separation in such a system depends not only on the size, but also the shape of the protein molecules.