Magnetic resonance imaging (MRI) gradient coils produce acoustic noise due to coil conductor vibrations caused by large Lorentz forces. Accurate sound pressure levels and modeling of heating are essential for the assessment of gradient coil safety. This work reviews the state-of-the-art numerical methods used in accurate gradient coil modeling and prediction of sound pressure levels (SPLs) and temperature rise. We review several approaches proposed for noise level reduction of high-performance gradient coils, with a maximum noise reduction of 20 decibels (dB) demonstrated. An efficient gradient cooling technique is also presented.