Short tandem repeats (STRs) are units of 1-6 bp that repeat in a tandem fashion in DNA. Along with single nucleotide polymorphisms and large structural variations, they are among the major genomic variants underlying genetic, and likely phenotypic, divergence. STRs experience mutation rates that are orders of magnitude higher than other well-studied genotypic variants. Frequent copy number changes result in a wide range of alleles, and provide unique opportunities for modulating complex phenotypes through variation in repeat length. While classical studies have identified key roles of individual STR loci, the advent of improved sequencing technology, high-quality genome assemblies for diverse species, and bioinformatics methods for genome-wide STR analysis now enable more systematic study of STR variation across wide evolutionary ranges. In this review, we explore mutation and selection processes that affect STR copy number evolution, and how these processes give rise to varying STR patterns both within and across species. Finally, we review recent examples of functional and adaptive changes linked to STRs.