Dynamic processes at the solid-liquid interface are of key importance across broad areas of science and technology. Electrochemical deposition of copper, for example, is used for metallization in integrated circuits, and a detailed understanding of nucleation, growth and coalescence is essential in optimizing the final microstructure. Our understanding of processes at the solid-vapour interface has advanced tremendously over the past decade due to the routine availability of real-time, high-resolution imaging techniques yielding data that can be compared quantitatively with theory. However, the difficulty of studying the solid-liquid interface leaves our understanding of processes there less complete. Here we analyse dynamic observations--recorded in situ using a novel transmission electron microscopy technique--of the nucleation and growth of nanoscale copper clusters during electrodeposition. We follow in real time the evolution of individual clusters, and compare their development with simulations incorporating the basic physics of electrodeposition during the early stages of growth. The experimental technique developed here is applicable to a broad range of dynamic phenomena at the solid-liquid interface.