Nonlinear multivariate analysis of neurophysiological signals is a critical tool for understanding the complex interactions between simultaneously recorded signals in neurophysiology. This review discusses various methods for analyzing these interactions, including linear and nonlinear techniques, and highlights their applications in neurophysiological data. The paper begins by describing traditional linear methods such as cross-correlation, coherence, and Granger causality, which are used to assess linear relationships between signals. It then moves on to nonlinear methods, including mutual information, transfer entropy, phase synchronization, generalized synchronization, and event synchronization. These methods are particularly useful for detecting nonlinear interdependencies and directional coupling between signals. The paper emphasizes the importance of using multivariate surrogate data to assess the strength and type of interdependence between signals. It also discusses the limitations of linear methods in capturing nonlinear features of neurophysiological data and the need for more sophisticated techniques. The review covers a wide range of applications, from EEG and MEG data to spike trains, and highlights the utility of these methods in understanding brain function and pathology. The paper concludes with a comparison of different approaches and practical considerations for their application in neurophysiological research. The authors also provide appendices that explain the use of multivariate surrogate data and practical guidelines for implementing these methods. Overall, the paper provides a comprehensive overview of the current state of nonlinear multivariate analysis in neurophysiology and its potential for advancing our understanding of brain function.Nonlinear multivariate analysis of neurophysiological signals is a critical tool for understanding the complex interactions between simultaneously recorded signals in neurophysiology. This review discusses various methods for analyzing these interactions, including linear and nonlinear techniques, and highlights their applications in neurophysiological data. The paper begins by describing traditional linear methods such as cross-correlation, coherence, and Granger causality, which are used to assess linear relationships between signals. It then moves on to nonlinear methods, including mutual information, transfer entropy, phase synchronization, generalized synchronization, and event synchronization. These methods are particularly useful for detecting nonlinear interdependencies and directional coupling between signals. The paper emphasizes the importance of using multivariate surrogate data to assess the strength and type of interdependence between signals. It also discusses the limitations of linear methods in capturing nonlinear features of neurophysiological data and the need for more sophisticated techniques. The review covers a wide range of applications, from EEG and MEG data to spike trains, and highlights the utility of these methods in understanding brain function and pathology. The paper concludes with a comparison of different approaches and practical considerations for their application in neurophysiological research. The authors also provide appendices that explain the use of multivariate surrogate data and practical guidelines for implementing these methods. Overall, the paper provides a comprehensive overview of the current state of nonlinear multivariate analysis in neurophysiology and its potential for advancing our understanding of brain function.