Radiofrequency magnetic fields are critical to nuclear excitation and signal reception in magnetic resonance imaging. The interactions between these fields and human tissues in anatomical geometries results in a variety of effects regarding image integrity and safety of the human subject. In recent decades, numerical methods of calculation have been used increasingly to understand the effects of these interactions and aid in engineering better, faster, and safer equipment and methods. As magnetic resonance imaging techniques and technology have evolved through the years, so to have the requirements for meaningful interpretation of calculation results. Here, we review the basic physics of radiofrequency electromagnetics in magnetic resonance imaging and discuss a variety of ways radiofrequency field calculations are used in magnetic resonance imaging in engineering and safety assurance from simple systems and sequences through advanced methods of development for the future. Magn Reson Med, 2011. © 2011 Wiley-Liss, Inc.