  This article provides a concise overview of some of the recent advances in
the application of rough path theory to machine learning. Controlled
differential equations (CDEs) are discussed as the key mathematical model to
describe the interaction of a stream with a physical control system. A
collection of iterated integrals known as the signature naturally arises in the
description of the response produced by such interactions. The signature comes
equipped with a variety of powerful properties rendering it an ideal feature
map for streamed data. We summarise recent advances in the symbiosis between
deep learning and CDEs, studying the link with RNNs and culminating with the
Neural CDE model. We concluded with a discussion on signature kernel methods.
