The field of coordination polymers and metal–organic frameworks has to date focused on the crystalline state. More than 60,000 crystalline metal–organic framework structures, formed from highly ordered arrays of metal nodes connected by organic ligands in at least one dimension, have been identified. However, interest in non-crystalline systems is growing, with amorphous solids, glasses and liquids identified as possessing similar metal–ligand bonding motifs to their crystalline cousins. In this Review, we provide an overview of the structural design, properties and potential applications of non-crystalline coordination polymers and metal–organic frameworks. In particular, we highlight recent reports of glasses that result from the melt quenching of the liquid states of these topical classes of materials. Finally, we provide a perspective on the future of the non-crystalline domain of coordination polymers and metal–organic frameworks. There is increasing interest in the liquid, glass and amorphous solid states of coordination polymers and metal–organic frameworks. In this Review, we discuss the background and terminology of this emerging field, categorize example structures and provide an outlook for the future direction of the field.