A large literature on the sensitivity of streamflow response to climate variations has emerged over the past several decades, but the underlying mechanisms are not fully understood. The usual approaches to this problem have been simple and do not fully address its complexity, which involves the individual and joint effects of large‐scale climate modes and smaller‐scale weather features on streamflow volumes, the presence of persistence in these time series and their effects on antecedent conditions. Ongoing improvements in observational and reanalysis datasets and online access allow for better quantification of the connections between streamflow response, climate variability modes and regional weather features. The purpose of this paper is to determine whether Bayesian networks can be used to better identify key factors and their associated pathways leading to streamflow generation. A Markov blanket approach is described and illustrated using monthly streamflow series recorded at eight gauging stations within or immediately adjacent to the coastal region of eastern mainland Australia. The method is compared and contrasted with conventional multiple linear regression with discussion around this type of approach as part of a growing interest in machine learning applications. One example is used to illustrate the application of both approaches to a streamflow series exhibiting strong non‐stationarity. Results for the other streamflow series are included in a concise synthesis. Overall, the results suggest that Bayesian networks have several desirable features in terms of transparency, interpretability and explanatory insight. The findings from this study lend support to the use of Bayesian networks for modelling connections between streamflow volume and the variability of climate and regional weather. This improved understanding of the key controls of streamflow variability is intended to help address growing needs around informing social, cultural, economic and ecological aspects of water planning and management. [ABSTRACT FROM AUTHOR]