A bstract In negatively curved field spaces, inflation can be realised even in steep potentials. Hyperinflation invokes the ‘centrifugal force’ of a field orbiting the hyperbolic plane to sustain inflation. We generalise hyperinflation by showing that it can be realised in models with any number of fields ( N f ≥ 2), and in broad classes of potentials that, in particular, don’t need to be rotationally symmetric. For example, hyperinflation can follow a period of radial slow-roll inflation that undergoes geometric destabilisation, yet this inflationary phase is not identical to the recently proposed scenario of ‘side-tracked inflation’. We furthermore provide a detailed proof of the attractor mechanism of (the original and generalised) hyperinflation, and provide a novel set of characteristic, explicit models. We close by discussing the compatibility of hyperinflation with observations and the recently much discussed ‘swampland conjectures’. Observationally viable models can be realised that satisfy either the ‘de Sitter conjecture’ ( V ′ /V ≳ 1) or the ‘distance conjecture’ (Δ ϕ ≲ 1), but satisfying both simultaneously brings hyperinflation in some tension with successful reheating after inflation. However, hyperinflation can get much closer to satisfying all of these criteria than standard slow-roll inflation. Furthermore, while the original model is in stark tension with the weak gravity conjecture, generalisations can circumvent this issue.