Microwaves are a form of electromagnetic radiation commonly used for telecommunications, navigation and food processing. More recently microwave technologies have found applications in fibre-reinforced polymer composites, which are increasingly used in aircraft structures. Microwave energy can be applied with low power (up to milliwatts) for non-destructive testing and high power (up to kilowatts) for heating/curing purposes. The state-of-the-art applications at high power include curing, three-dimensional (3D) printing, joining and recycling, whereas low-power microwave techniques can provide quality checks, strain sensing and damage inspection. Low-power microwave testing has the advantage of being non-contact, there is no need for surface transducers or couplants, it is operator friendly and relatively inexpensive; high-power microwave energy can offer volumetric heating, reduced processing time and energy saving with no ionising hazards. In this paper the recent research progress is reviewed, identifying achievements and challenges. First, the critical electromagnetic properties of composites that are closely related to the heating and sensing performance are discussed. Then, representative case studies are presented. Finally, the trends are outlined, including intelligent/automated inspection and solid-state heating.