Abstract Cross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and physiological interpretation come with fundamental problems. For example, apparent CFC can appear because of spectral correlations due to common non-stationarities that may arise in the total absence of interactions between neural frequency components. To provide a road map towards an improved mechanistic understanding of CFC, we organize the available and potential novel statistical/modeling approaches according to their biophysical interpretability. While we do not provide solutions for all the problems described, we provide a list of practical recommendations to avoid common errors and to enhance the interpretability of CFC analysis. Highlights Fundamental caveats and confounds in the methodology of assessing CFC are discussed. Significant CFC can be observed without any underlying physiological coupling. Non-stationarity of a time-series leads to spectral correlations interpreted as CFC. We offer practical recommendations, which can relieve some of the current confounds. Further theoretical and experimental work is needed to ground the CFC analysis.