Static and kinetic friction play a fundamental role in sea-ice mechanics. The coefficient of static friction increases with hold time under normal load and is modelled in terms of creep and fracture of asperities in contact. The coefficient of kinetic friction exhibits velocity strengthening at lower speeds and velocity weakening at intermediate speeds. Strengthening is modelled in terms of asperity creep and hardness; weakening is modelled in terms of a progressive increase in the true area of contact wetted by meltwater produced through frictional heating. The concept is introduced of contact size distribution in which the smallest contacts melt first, leading to the onset of weakening; the largest melt last, leading to a third regime of kinetic friction and again to strengthening where hydrodynamics governs. Neither the static nor the kinetic coefficient is significantly affected by the presence of sea water. The paper closes with a few implications for sea-ice mechanics. The paper is based largely upon a critical review of the literature, but includes a more quantitative, physics-based analysis of velocity strengthening and a new analysis of velocity weakening that incorporates parameters that describe the (proposed) fractal character of the sliding interface.This article is part of the theme issue ‘Modelling of sea-ice phenomena’.