Preoperative localization of functionally eloquent cortex (functional cortical mapping) is common clinical practice in order to avoid or reduce postoperative morbidity. This review aims at providing a general overview of magnetoencephalography (MEG) and high-density electroencephalography (hdEEG) based methods and their clinical role as compared to common alternatives for functional cortical mapping of (1) verbal language function, (2) sensorimotor cortex, (3) memory, (4) visual, and (5) auditory cortex. We highlight strengths, weaknesses and limitations of these functional cortical mapping modalities based on findings in the recent literature. We also compare their performance relative to other non-invasive functional cortical mapping methods, such as functional Magnetic Resonance Imaging (fMRI), Transcranial Magnetic Stimulation (TMS), and to invasive methods like the intracarotid Amobarbital Test (WADA-Test) or intracranial investigations.