In this contribution, we propose a review of the possible implications of hydrogen on mechanical behaviour of Zr and Ti alloys with emphasis on the mechanisms of plasticity and strain hardening. Recent advances on the impact of oxygen and hydrogen on the activation volume show that oxygen content hinders creep but hydrogen partially screens this effect. Both aspects are discussed in terms of a locking-unlocking model of the screw dislocation mobility in prismatic slip. Additionally, possible extension of this behaviour is suggested for the [Formula: see text] pyramidal slip. The low hydrogen solubility in both Zr and Ti leads in many cases to hydride precipitation. The nature of these phases depends on the hydrogen content and can show crystallographic orientation relationships with the hexagonal compact structure of the alloys. Some advances on the thermal stability of these phases are illustrated and discussed in relation with the deepening of the misfit dislocations. Under tensile loading, we showed that hydrides enhance the hardening process in relation with internal stress due to strain incompatibilities between the Zr and Ti matrix and hydride phases. Different plastic yielding processes of hydrides were identified, which progressively reduce these strain incompatibilities.This article is part of the themed issue 'The challenges of hydrogen and metals'.