Articulating disc implant

A method of delivering and positioning an intervertebral implant into an intervertebral space between a superior vertebra and an inferior vertebra, the method comprising:

• engaging a first articulating surface of an upper part of the implant with a second articulating surface of a lower part of the implant, such that the first articulating surface defines a first radius of curvature in a first direction and a second radius of curvature in a second direction that is perpendicular to the first direction, and the second articulating surface defining a third radius of curvature in the first direction and a fourth radius of curvature in the second direction;
• after the engaging step, inserting the intervertebral implant into the intervertebral disc space along an anterior-posterior direction such that a first surface of the upper part that is spaced from the first articulating surface engages an endplate of the superior vertebra, a second surface of the lower part that is spaced from the second articulating surface engages an endplate of the inferior vertebra, the first and third radii of curvature are substantially equal along the anterior-posterior direction, and one of the second and fourth radii of curvature varies along a medial-lateral direction that is perpendicular to the anterior-posterior direction.