Basal thumb joint implant has a head with a smooth, generally hemispherical, medio-proximally directed, articulating surface, and a generally abrupt, distally directed, truncation thereto; and a stem attached to the head, which arises from the truncation of the head and includes at least one of the following features: A) a general angle of attachment to the head which is acute in relation to the truncation of the head; B) a flanged cross-sectional stem profile; C) an inwardly curved stem; D) an eccentric head attachment site for the stem. The implant may be one-piece or modular in construction. The modular basal thumb joint implant, however, which is not necessarily limited by requiring inclusion of the aforesaid additional features A-D, includes a head with a smooth, generally hemispherical, medio-proximally directed, articulating surface, a generally abrupt, distally directed truncation thereto, and a stem trunion-receiving cup in the truncation; and a stem attachable to the head, which stem has intracarpal spike-like distal end, and a proximally directed trunion, which trunion is insertable into the stem trunion-receiving cup of the head. Other digits may be provided with analogous implants, particularly with respect to those digital implants amenable to modularity.