Natural selection leaves distinct signatures in the genome that can reveal the targets and history of adaptive evolution. By analysing high-coverage genome sequence data from 4 major colour pattern loci sampled from nearly 600 individuals in 53 populations, we show pervasive selection on wing patterns in the Heliconius adaptive radiation. The strongest signatures correspond to loci with the greatest phenotypic effects, consistent with visual selection by predators, and are found in colour patterns with geographically restricted distributions. These recent sweeps are similar between co-mimics and indicate colour pattern turn-over events despite strong stabilising selection. Using simulations, we compare sweep signatures expected under classic hard sweeps with those resulting from adaptive introgression, an important aspect of mimicry evolution in Heliconius butterflies. Simulated recipient populations show a distinct 'volcano' pattern with peaks of increased genetic diversity around the selected target, characteristic of sweeps of introgressed variation and consistent with diversity patterns found in some populations. Our genomic data reveal a surprisingly dynamic history of colour pattern selection and co-evolution in this adaptive radiation.