An intervertebral prosthesis which is designed to be at least partially received within an intervertebral disc space. The intervertebral disc space is defined between an end plate of a first vertebral body and an adjacent end plate of a second, adjacent vertical body. The prosthesis comprises a first component which is designed to be attached to the first vertebral body and a second component which is designed to be attached to the second vertebral body. The first and second components comprise surfaces which, in use, are directed towards the opposing end plate and which extend substantially entirely across the part of the component which is received within the intervertebral disc space. The surfaces of both the first and second components define respective monotonic curves which have no discontinuities therein.