The aim of this article is to put forward the novel concept of porous liquids, or, more precisely, liquids with permanent microporosity. In contrast to the small, transient cavities that exist between the molecules of any liquid (here called "extrinsic" porosity), we suggest that a truly microporous liquid could exist if it had empty pores within the molecules of the liquid ("intrinsic" porosity). By using rigid host molecules with restricted access windows, any unwanted occupation of the pores could be prevented (i.e., the pores could be kept empty and available so that the liquid would be genuinely microporous). The liquid could have permanent, well-defined, empty pores capable of molecular recognition when exposed to other species (e.g., gases etc.). We stress that these phases are not the same as simple solutions of host species, in which any pores would normally be occupied by solvent molecules. In microporous liquids, any solvent molecules, if present, would be deliberately sterically excluded from the host cavities, to leave them readily accessible. Microporous liquids would be of considerable fundamental interest. They could combine properties of microporous solids, such as size- and shape-selective sorption and so forth, with the rapid mass transfer, fluidity and fast kinetics of liquids. Some synthetic approaches to these materials are discussed in this article. Also, whilst the overall concept of microporous liquids is new, literature is described which suggests that some examples have arguably already been reported, even if they have not previously been recognised and characterised in such terms.