<p>Formamide, the simplest amide, forms an ambient-pressure crystal structure consisting of stacks of NH⋯O hydrogen-bonded layers. Here we report the effect of pressure extending to a maximum of 3.6 GPa on the crystal structures of formamide-<i>h</i>₃ and formamide-<i>d</i>₃ using single-crystal X-ray diffraction and neutron powder diffraction, revealing previously unrecognised but extensive phase diversity between ambient pressure and 1.81 GPa. The crystal structures of five distinct crystalline phases, designated I_α (the known ambient pressure phase), II, III, IV_β (also known from previous work) and V, have been determined. The pressures and isotopologues of the determinations were 0.20 GPa (for <i>h</i>₃ phase I_α), 0.20 and 0.36 GPa (for the <i>d</i>₃ and <i>h</i>₃ forms of phase II), 0.35 GPa (<i>d</i>₃ form of phase III), 0.43 and 0.78 GPa (for the <i>h</i>₃ and <i>d</i>₃ forms of IV_β) and 1.81 GPa (<i>d</i>₃ form of phase V). All phases contain NH⋯O hydrogen-bonded chain motifs, with phases III and IV_β being layered structures similar to I_α, but phases II and V forming 3-dimensional networks. The architectures are determined by whether a hydrogen-bonded chain utilises the oxygen lone pair cis or trans to the amide nitrogen and the orientations of the molecules. The phases conform to well-known topological types, I_α, II and IV_β being based on cubic close packing while phase V is a distorted form of the same topology, reflecting denser packing at elevated pressure. Phase III can be considered to have a body centred cubic topology. Pixel packing energy calculations show that competing H-bonding arrangements are energetically comparable even when they deviate from an ideal H-bonding geometry, while non-H-bonding contacts, including antiparallel stacking and aldehyde–aldehyde interactions, contribute additional stabilisation, also with notable geometric flexibility.</p> Graphical Abstract <p></p>