RAD51 recombinase assembles on single-stranded (ss)DNA substrates exposed by DNA end-resection to initiate homologous recombination (HR), a process fundamental to genome integrity. RAD51 assembly has been characterized using purified proteins, but its ultrastructural topography in the cell nucleus is unexplored. Here, we combine cell genetics with single-molecule localization microscopy and a palette of bespoke analytical tools, to visualize molecular transactions during RAD51 assembly in the cellular milieu at resolutions approaching 30-40 nm. In several human cell types, RAD51 focalizes in clusters that progressively extend into long filaments, which abut-but do not overlap-with globular bundles of replication protein A (RPA). Extended filaments alter topographically over time, suggestive of succeeding steps in HR. In cells depleted of the tumor suppressor protein BRCA2, or overexpressing its RAD51-binding BRC repeats, RAD51 fails to assemble at damage sites, although RPA accumulates unhindered. By contrast, in cells lacking a BRCA2 carboxyl (C)-terminal region targeted by cancer-causing mutations, damage-induced RAD51 assemblies initiate but do not extend into filaments. We suggest a model wherein RAD51 assembly proceeds concurrently with end-resection at adjacent sites, via an initiation step dependent on the BRC repeats, followed by filament extension through the C-terminal region of BRCA2.