This disclosure relates to intervertebral disc prostheses which may have an upper plate, a lower plate, and a mobile core, with the upper surface of the core being in contact with at least a part of the lower surface of the upper plate. In some configurations, limit stops reduce friction while limiting or preventing the movements of the core relative to the lower plate, in translation and in rotation, respectively, along an axis substantially parallel to the lower plate and about an axis substantially perpendicular to the lower plate. Instrumentation for insertion of the prostheses into intervertebral spaces is also described.