During the past decade, phase separation has emerged as a main driver of the self-organizing processes taking place in eukaryotic cells, whereby membranes and other biological components acquire specific chemical identities, corresponding to distinct biological functions. Most often, such processes are ??active??, i.e. they involve the action of energy-consuming enzymatic reactions. The aim of this thesis is to study a minimal model of active domain formation on cell membranes, combining an analytical approach and numerical computations. We derive a mean-field phase diagram identifying parameter regions where the membrane system tends to demix by either a nucleation process or by spinodal decomposition.