Porous materials contain regions of empty space into which guest molecules can be selectively adsorbed and sometimes chemically transformed. This has made them useful in both industrial and domestic applications, ranging from gas separation, energy storage and ion exchange to heterogeneous catalysis and green chemistry. Porous materials are often ordered (crystalline) solids. Order — or uniformity — is frequently held to be advantageous, or even pivotal, to our ability to engineer useful properties in a rational way. Here we highlight the growing evidence that topological disorder can be useful in creating alternative properties in porous materials. In particular, we highlight here several concepts for the creation of novel porous liquids, rationalize routes to porous glasses and provide perspectives on applications for porous liquids and glasses.