While metal–organic frameworks have been mostly studied in their crystalline form, recent advances were made on their amorphous phases both in fundamental understanding and in relation to potential applications. In particular, the zeolitic imidazolate framework (ZIF) glasses, that can be obtained from quenching liquid ZIFs, have shown promise. However, the details of their microscopic structure are very hard to probe experimentally. Here, we use ab initio molecular dynamics simulations to investigate the nature of ZIF glasses obtained from quenching molten ZIFs in silico. Through computational modeling of the melt–quench process on three different ZIF crystals, we aim to understand the effect of topology and chemistry upon the structure of the glass, compared to both the crystalline precursor and the high-temperature liquid. We report here the first direct computational description of MOF glasses at the quantum chemical level. We find that both the chemical nature of the imidazolate linker and the topology of the framework play a role in the behavior upon quenching and the properties of the glasses obtained: structure, average coordination, and pore space.