Multiple studies have now demonstrated that machine learning (ML) can give improved skill for predicting or simulating fairly typical weather events, for tasks such as short-term and seasonal weather forecasting, downscaling simulations to higher resolution and emulating and speeding up expensive model parameterisations. Many of these used ML methods with very high numbers of parameters, such as neural networks, which are the focus of the discussion here. Not much attention has been given to the performance of these methods for extreme event severities of relevance for many critical weather and climate prediction applications, with return periods of more than a few years. This leaves a lot of uncertainty about the usefulness of these methods, particularly for general purpose prediction systems that must perform reliably in extreme situations. ML models may be expected to struggle to predict extremes due to there usually being few samples of such events. However, there are some studies that do indicate that ML models can have reasonable skill for extreme weather, and that it is not hopeless to use them in situations requiring extrapolation. This article reviews these studies and argues that this is an area that needs researching more. Ways to get a better understanding of how well ML models perform at predicting extreme weather events are discussed.