Radiofrequency (RF) coils are key components of magnetic resonance imaging (MRI) systems. The primary purpose of this review is to provide a basic theory of RF coil designs and their characterization by bench measurements, electromagnetic field simulations and MR measurements. With the continuing increase of magnetic field strength in MRI instruments, the RF wavelength in the subject under study becomes comparable to or smaller in size than the anatomical dimensions of the tissue under study, which amplifies the signal inhomogeneity. Also, RF energy increases quadratically with the Larmor frequency, which leads to increased heat deposition in the subject, especially at ultra-high field. Elegant RF coil designs are explored here to address these challenges.