Astronomical objects that change rapidly give us insight into extreme environments, allowing us to identify new phenomena, test fundamental physics, and probe the Universe on all scales. Transient and variable radio sources range from the cosmological, such as gamma-ray bursts, to much more local events, such as massive flares from stars in our Galactic neighbourhood. The capability to observe the sky repeatedly, over many frequencies and timescales, has allowed us to explore and understand dynamic phenomena in a way that has not been previously possible. In the past decade, there have been great strides forward as we prepared for the revolution in time domain radio astronomy that is being enabled by the SKA Observatory telescopes, the SKAO pathfinders and precursors, and other ‘next generation’ radio telescopes. Hence it is timely to review the current status of the field, and summarise the developments that have happened to get to our current point. This review focuses on image domain (or ‘slow’) transients, on timescales of seconds to years. We discuss the physical mechanisms that cause radio variability, and the classes of radio transients that result. We then outline what an ideal image domain radio transients survey would look like, and summarise the history of the field, from targeted observations to surveys with existing radio telescopes. We discuss methods and approaches for transient discovery and classification, and identify some of the challenges in scaling up current methods for future telescopes. Finally, we present our current understanding of the dynamic radio sky, in terms of source populations and transient rates, and look at what we can expect from surveys on future radio telescopes.