Prostheses, systems, and methods are provided for replacement of natural facet joints between adjacent vertebrae using polyaxial attachment mechanisms for securing the prostheses to the vertebrae. A cephalad prosthesis attached to a superior adjacent vertebra replaces the inferior half of a natural facet joint. A caudal prosthesis attached to an inferior adjacent vertebra replaces the superior half of a natural facet joint. Both the cephalad and caudal prostheses are configured with artificial facet joint structures that include articulating surfaces that cooperate and form an artificial articular configuration. The polyaxial attachment mechanism permits adjustment of the position of the artificial facet joint structure along more than one axis at or after the time the cephalad or caudal prosthesis is attached to a vertebra.