Recent experimental studies of compressive failure in fibre-reinforced polymeric composites have been analysed. It is shown that the parametric basis for most compressive strength models, i.e. pure plastic buckling controlled by matrix shear strength and initial fibre misorientation, is probably incomplete. It is argued that, instead, failure is triggered by the initiation of an unstable kink band prior to buckling instability, and that additional parameters (interfacial shear stress/strain; fibre strength) are responsible for this transition in mechanisms.