The design of optimized radiofrequency (RF) coils is a fundamental task for maximizing the signal-to-noise ratio (SNR) in Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spectroscopy (MRS) applications. An efficient coil should be designed by minimizing the coil noise with respect to the sample noise, since coil conductor resistance affects data quality by reducing the SNR, especially for coils tuned to a low frequency. Such conductor losses strongly depend on the frequency (due to the skin effect) and on the conductor cross-sectional shape (strip or wire). This paper reviews the different methods for estimating conductor losses in RF coils for MRI/MRS applications, comprising analytical formulations, theoretical/experimental hybrid approaches and full-wave simulations. Moreover, the different strategies for minimizing such losses, including the use of Litz wire, cooled and superconducting coils, are described. Finally, recent emerging technologies in RF coil design are briefly reviewed.