The principles of engineering and physics have been applied to oncology for nearly 50 years. Engineers and physical scientists have made contributions to all aspects of cancer biology, from quantitative understanding of tumour growth and progression to improved detection and treatment of cancer. Many early efforts focused on experimental and computational modelling of drug distribution, cell cycle kinetics and tumour growth dynamics. In the past decade, we have witnessed exponential growth at the interface of engineering, physics and oncology that has been fuelled by advances in fields including materials science, microfabrication, nanomedicine, microfluidics, imaging, and catalysed by new programmes at the National Institutes of Health (NIH), including the National Institute of Biomedical Imaging and Bioengineering (NIBIB), Physical Sciences in Oncology, and the National Cancer Institute (NCI) Alliance for Nanotechnology. Here, we review the advances made at the interface of engineering and physical sciences and oncology in four important areas: the physical microenvironment of the tumour and technological advances in drug delivery; cellular and molecular imaging; and microfluidics and microfabrication. We discussthe research advances, opportunities and challenges for integrating engineering and physical sciences with oncology to develop new methods to study, detect and treat cancer, and we also describe the future outlook for these emerging areas.