Extant genomes are largely shaped by the global transposition, copy number fluctuation, and rearrangement of DNA sequences, rather than by the substitutions of single nucleotides. Although many of these large-scale mutations have low probabilities and are unlikely to repeat, others are recurrent or predictable in their effects, leading to stereotyped genome architectures and genetic variation in both eukaryotes and prokaryotes. Such recurrent, parallel mutation modes can profoundly shape the paths taken by evolution, and directly undermine the Wright-Fisher model of evolutionary genetics. Similar patterns are also evident at the smaller scales of individual genes or short genomic sequences. The scale and extent of this ‘non-substitution’ variation has only recently come into focus through the advent of new genomic technologies; however, it still not widely included in genotype-phenotype association studies. In this review, we identify the common features of these disparate mutational phenomena and comment on the importance and interpretation of these mutational patterns