Homologous recombination (HR) is a major pathway to repair DNA double-strand breaks (DSB). HR uses an undamaged homologous DNA sequence as a template for copying the missing information, which requires identifying a homologous sequence among megabases of DNA within the crowded nucleus. In eukaryotes, the conserved Rad51-ssDNA nucleoprotein filament (NPF) performs this homology search. Although NPFs have been extensively studied in vitro by molecular and genetic approaches, their in vivo formation and dynamics could not thus far be assessed due to the lack of functional tagged versions of Rad51. Here, we develop and characterize in budding yeast the first fully functional, tagged version of Rad51. Following induction of a unique DSB, we observe Rad51-ssDNA forming exceedingly long filaments, spanning the whole nucleus and eventually contacting the donor sequence. Emerging filaments adopt a variety of shapes, not seen in vitro and are modulated by Rad54 and Srs2, shedding new light on the function of these factors. The filaments are also surprisingly dynamic, undergoing rounds of compaction and extension. Our biophysical models demonstrate that formation of extended filaments, and particularly their compaction-extension dynamics, constitute a robust search strategy, allowing DSB to rapidly explore the nuclear volume and thus enable efficient HR.