This chapter describes the design of radiofrequency coils for high resolution liquid- and solid-state NMR, animal MRI and MR microscopy, and human MRI at clinical and ultra-high field strengths. Concepts of transmit and receive magnetic fields, linear and circular polarization, conservative and non-conservative electric fields, impedance matching, multiple-frequency tuning, and coil loading are introduced. Specific designs covered include birdcage coils and TEM resonators, surface coils, microcoils, transmit and receive arrays, and dielectric resonators.