The subseasonal Madden-Julian oscillation (MJO) is among the most important modes of tropical variability on the planet and is a dominant driver of subseasonal-to-seasonal (S2S) prediction globally. The past decade has seen substantial advances in MJO prediction using dynamical forecast models, which now routinely outperform traditional statistical MJO forecasts (e.g. multiple linear regression models). At the same time, an increasing body of literature has demonstrated that machine-learning methods represent a new frontier in Earth science, opening the door to more advanced statistical forecast models of the MJO. In this study, we explore whether state-of-the-art machine learning methods can be used to make real-time MJO forecasts that outperform traditional statistical models and do comparably well to dynamical models. In particular, we utilize neural networks trained on observational tropical fields to attempt to make skillful forecasts of MJO convection out to several weeks lead time. Through contrasting the machine-learning models’ behavior with simpler statistical models and dynamical forecast models, we explore the advantages and disadvantages of statistical versus dynamical forecasts. A novel aspect of our analysis is the use of cutting-edge techniques to allow us to visualize how our neural network models makes their predictions. These techniques, such as layer-wise relevance propagation, can lead to new insights into regions of MJO predictability, allowing us to better interpret sources of MJO prediction skill within the machine-learning model. We further diagnose whether our machine-learning models contain well-known aspects of MJO prediction found in dynamical models, such as an increase in prediction skill during boreal winter or during certain phases of the stratospheric quasi-biennial oscillation.