The unique features of HTS offer opportunities and challenges to a number of applications. In this paper we focus on NMR and MRI magnets, illustrating them with the NMR/MRI magnets that we are currently and will shortly be engaged: a 1.3 GHz NMR magnet, an "annulus" magnet, and an $MgB_2$whole-body MRI magnet. The opportunities with HTS include: 1) high fields (e.g., 1.3 GHz magnet); 2) compactness (annulus magnet); and 3) enhanced stability despite liquid-helium-free operation ($MgB_2$whole-body MRI magnet). The challenges include: 1) a large screening current field detrimental to spatial field homogeneity (e.g., 1.3 GHz magnet); 2) uniformity of critical current density (annulus magnet); and 3) superconducting joints ($MgB_2$magnet).