This paper provides a comprehensive review of multivariate time series analysis methods used in neurophysiology to study the relationships between simultaneously recorded signals. It begins by discussing traditional linear methods, such as cross-correlation and coherence, and then moves to nonlinear methods based on concepts like phase synchronization, generalized synchronization, and event synchronization. The authors also explore information-theory-based methods, including mutual information and transfer entropy, and discuss the use of multivariate surrogate data to assess the strength and type of interdependence between signals. The paper highlights the advantages and limitations of each method and provides practical guidelines for their application to neurophysiological data, such as EEG and MEG signals. Finally, it compares the performance of different nonlinear methods and offers insights into the complex dynamics of neural systems.This paper provides a comprehensive review of multivariate time series analysis methods used in neurophysiology to study the relationships between simultaneously recorded signals. It begins by discussing traditional linear methods, such as cross-correlation and coherence, and then moves to nonlinear methods based on concepts like phase synchronization, generalized synchronization, and event synchronization. The authors also explore information-theory-based methods, including mutual information and transfer entropy, and discuss the use of multivariate surrogate data to assess the strength and type of interdependence between signals. The paper highlights the advantages and limitations of each method and provides practical guidelines for their application to neurophysiological data, such as EEG and MEG signals. Finally, it compares the performance of different nonlinear methods and offers insights into the complex dynamics of neural systems.