Differential equations and neural networks are two of the most widespread modelling paradigms. I will talk about how to combine the best of both worlds through neural differential equations. Beginning with a brief overview of the broader field of neural differential equations (neural ODEs being the most famous example), I will then discuss recent work on neural controlled differential equations (neural CDEs) specifically. Intuitively these are "continuous time RNNs". These offer memory efficiency, the ability to handle irregular data, strong priors on model space, high capacity function approximation, and draw on a deep well of theory on both sides. They are state-of-the-art models for irregular time series, and if time allows I will briefly outline extensions for how they may be used to train neural SDEs.