Hybrid zones are established where two divergent populations meet and interbreed, but experience some reproductive isolation. If one population expands its range at the expense of the other, their hybrid zone moves. While hybrid zone movement is generally considered to be uncommon and insignificant, recent studies challenge this idea. The commonality of contemporary hybrid zone movement-with shifts in hybrid zones tracked over years to decennia-cannot be disputed, given the many examples available. Cases of historical hybrid zone movement-covering centuries or millennia of mobility-are accumulating, with movement having been inferred from five lines of evidence: (1) range shifts documented in the fossil/pollen record; (2) distribution dynamics derived from species distribution modelling; (3) enclaves of a displaced population persisting inside the range of an expanding one; (4) a peak of linkage disequilibrium at the leading edge of a moving hybrid zone; and (5) genome-wide genetic traces of a displaced population, left behind in an expanding one. While most of these lines of evidence are not straightforward to interpret and/or broadly applicable, the latter-a genomic footprint of hybrid zone movement-promises to be particularly suitable to determine whether a hybrid zone has been on the move since its inception. I argue that historical hybrid zone movement is likely to be prevalent and deserves wider acknowledgement in historical biogeography.