Most synthetic materials that show molecular-scale porosity consist of one-, two- or three-dimensional networks. Porous metal-organic frameworks in particular have attracted a lot of recent attention. By contrast, discrete molecules tend to pack efficiently in the solid state, leaving as little empty space as possible, which leads to non-porous materials. This Perspective discusses recent developments with discrete organic molecules that are porous in the solid state. Such molecules, which may be either crystalline or amorphous, can be categorized as either intrinsically porous (containing permanent covalent cavities) or extrinsically porous (inefficiently packed). We focus on the possible advantages of organic molecules over inorganic or hybrid systems in terms of molecular solubility, choice of components and functionalities, and structural mobility and responsiveness in non-covalent extended solids. We also highlight the potential for 'undiscovered' porous systems among the large number of cage-like organic molecules that are already known.