The motor nervous system transmits motion control information through nervous oscillations, which causes the synchronous oscillatory activity of the corresponding muscle to reflect the motion response information and give the cerebral cortex feedback, so that it can sense the state of the limbs. This synchronous oscillatory activity can reflect connectivity information of electroencephalography-electromyography (EEG-EMG) functional coupling. The strength of the coupling is determined by various factors including the strength of muscle contraction, attention, motion intention etc. It is very significant to study motor functional evaluation and control methods to analyze the changes of EEG-EMG synchronous coupling caused by different factors. This article mainly introduces and compares coherence and Granger causality of linear methods, the mutual information and transfer entropy of nonlinear methods in EEG-EMG synchronous coupling, and summarizes the application of each method, so that researchers in related fields can understand the current research progress on analysis methods of EEG-EMG synchronous systematically.