While much attention of the MOF community has been devoted to adsorption and purification of gases, there is now also a vast body of data on the capability of MOFs to separate and purify liquid mixtures. Initial studies focused on separation of petrochemicals in apolar backgrounds, but the attention has moved now to the separation of complex, e.g. chiral compounds, and to the isolation of biobased compounds from aqueous media. We here give an overview of most of the existing literature, with an accent on separation mechanisms and structure-selectivity relationships.