Quantitative electroencephalogram (qEEG) plays a significant role in EEG-based clinical diagnosis and studies of brain function. In past decades, various qEEG methods have been extensively studied. This article provides a detailed review of the advances in this field. qEEG methods are generally classified into linear and nonlinear approaches. The traditional qEEG approach is based on spectrum analysis, which hypothesizes that the EEG is a stationary process. EEG signals are nonstationary and nonlinear, especially in some pathological conditions. Various time-frequency representations and time-dependent measures have been proposed to address those transient and irregular events in EEG. With regard to the nonlinearity of EEG, higher order statistics and chaotic measures have been put forward. In characterizing the interactions across the cerebral cortex, an information theory-based measure such as mutual information is applied. To improve the spatial resolution, qEEG analysis has also been combined with medical imaging technology (e.g., CT, MR, and PET). With these advances, qEEG plays a very important role in basic research and clinical studies of brain injury, neurological disorders, epilepsy, sleep studies and consciousness, and brain function.