High-temperature superconductivity has a significant opportunity to improve the performance of nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) systems. The low rf losses and low operating temperatures of superconducting coils allow them to improve the signal-to-noise ratio in applications where the system noise dominates that of the sample under study. These improvements translate into new capabilities and shorter measurement times for NMR and MRI systems. In this pedagogical paper, we discuss the implementation and impact of high-T c superconducting thin films in rf coils for NMR and MRI applications.