The unique ability of magnetic resonance imaging to measure temperature noninvasively, in vivo, makes it an attractive tool for monitoring interventional procedures, such as radiofrequency or microwave ablation in real-time. The most frequently used approach for magnetic resonance-based temperature measurement is proton resonance frequency (PRF) thermometry. Although it has many advantages, including tissue-independence and real-time capability, the main drawback is its motion sensitivity. This is likely the reason PRF thermometry in moving organs, such as the liver, is not commonly used in the clinical arena. In recent years, however, several developments suggest that motion-corrected thermometry in the liver is achievable. The present article summarizes the diverse attempts to correct thermometry in the liver. Therefore, the physical principle of PRF is introduced, with additional references for necrosis zone estimation and how to deal with fat phase modulation, and main magnetic field drifts. The primary categories of motion correction are presented, including general methods for motion compensation and library-based approaches, and referenceless thermometry and hybrid methods. Practical validation of the described methods in larger patient groups will be necessary to establish accurate motion-corrected thermometry in the clinical arena, with the goal of complete liver tumor ablation.