The development of phased array transducers and their integration with magnetic resonance (MR) guidance and thermal monitoring has established transcranial MR-guided focused ultrasound (tcMRgFUS) as an attractive non-invasive modality for neurosurgical interventions. The presence of the skull, however, compromises the efficiency of transcranial FUS (tcFUS) therapy, as its heterogeneous nature and acoustic characteristics induce significant phase aberrations and energy attenuation, especially at the higher acoustic frequencies employed in tcFUS thermal therapy. These aberrations may distort and shift the acoustic focus as well as induce heating at the patient's scalp and skull bone. Phased array transducers feature hundreds of elements that can be driven individually, each with its own phase and amplitude. This feature allows for compensation of skull-induced aberrations by calculation and application of appropriate phase and amplitude corrections. In this paper, we illustrate the importance of precise refocusing and provide a comprehensive review of the wide variety of numerical and experimental techniques that have been used to estimate these corrections.