We introduce and motivate machine learning (ML) communications systems that aim to improve on and to even replace the vast expert knowledge in the field of communications using modern machine learning techniques. These have recently achieved breakthroughs in many different domains, but not yet in communications. By interpreting a communications system as an autoencoder, we develop a fundamental new way to think about radio communications system design as an end-to-end reconstruction optimization task that seeks to jointly optimize transmitter and receiver components in a single process. We further present the concept of Radio Transformer Networks (RTNs) as a means to incorporate expert domain knowledge in the ML model and study the application of convolutional neural networks (CNNs) on raw IQ time-series data for modulation classification. We conclude the paper with a deep discussion of open challenges and areas for future investigation.