Superconducting magnets for accelerators were first suggested in the mid-60’s and have since become one of the major components of modern particle colliders. Technological progress has been slow but steady for the last half-century, based primarily on Nb–Ti superconductor. That technology has reached its peak with the Large Hadron Collider (LHC). Despite the superior electromagnetic properties of Nb3Sn and adoption by early magnet pioneers, it is just now coming into use in accelerators though it has not yet reliably achieved fields close to the theoretical limit. The discovery of the High Temperature Superconductors (HTS) in the late ’80’s created tremendous excitement, but these materials, with tantalizing performance at high fields and temperatures, have not yet been successfully developed into accelerator magnet configurations. Thanks to relatively recent developments in both Bi-2212 and REBCO, and a more focused international effort on magnet development, the situation has changed dramatically. Early optimism has been replaced with a reality that could create a new paradigm in superconducting magnet technology. Using selected examples of magnet technology from the previous century to define the context, this paper will describe the possible innovations using HTS materials as the basis for a new paradigm.