Alfred Sturtevant, who invented genetic mapping while still an undergraduate, published the first evidence of a chromosomal inversion in 1921 [1]. He suggested then, and later proved, that they have a dramatic effect on transmission: when heterozygous, inversions suppress recombination. Over the next half century, inspired largely by Dobzhansky and his coworkers, much of empirical population genetics devoted itself to studying the abundant polymorphisms within and fixed differences of inversions between species of Drosophila [2]. Starting in the 1970s, this rich literature largely sank from view with the rise of biochemical and then molecular genetics. But inversions are ascendant again. Comparative genomics is now revealing that chromosomes are far more structurally fluid than even Dobzhansky dared to suppose. Where classic cytogenetics identified only nine inversions that distinguish humans and chimpanzees, comparison of their genomic sequences reveals on the order of 1,500 [3] (Figure 1). Despite the importance of inversions as a major mechanism for reorganizing the genome, we are still struggling to understand how and why they evolve almost a century after Sturtevant's discovery. Figure 1 Chromosome inversions that distinguish humans and chimpanzees inferred from a comparison of their genomic sequences [3]. An inversion occurs when a chromosome breaks at two points and the segment bounded by the breakpoints is reinserted in the reversed orientation. Several molecular mechanisms can mediate this event [4]. Box 1 gives an overview of some basic properties of inversions and the ways that they are detected. Box 1. What are chromosome inversions? Inversions are a diverse class of chromsomal mutation. The majority are small (<1KB) [3]. Others, for example the famous 3RP inversion of Drosophila melanogaster, are several megabases in size, include several percent of the entire genome and span hundreds or thousands of genes [10]. Inversions fall into two classes: pericentric inversions include a centromere, while paracentric inversions do not. With pericentric inversions, a single crossover event that occurs between the breakpoints of a heterozygote produces unbalanced gametes that carry deletions, insertions, and either zero or two centromeres. This can reduce fertility, making the inversions underdominant (lowered heterozygote fitness). Some pericentric inversions apparently escape fitness costs when heterozygous, however, perhaps because they somehow suppress recombination [33]. Although these may represent but a small fraction of all pericentric inversions that arise by mutation, they are likely to be greatly enriched among those that spread to fixation. There are large systematic differences between taxa in the frequency and severity of fitness effects. For example, heterozygotes for inversions seem to show decreased fertility in plants much more commonly than in animals [10]. By contrast, many of the paracentric inversions segregating in nature may not suffer from underdominance. This is likely a major reason why they are orders of magnitude more common than pericentric inversions, both as polymorphisms within and fixed differences between species [33]. Inversions were first seen in the giant salivary chromosomes of larval flies, and Diptera remains the group in which large inversions can be most easily detected. Chromosome staining techniques are able to visualize inversions in some other groups, including mammals, but with much lower resolution (and greater effort). The presence of an inversion is suggested when a certain cross consistently shows blocked recombination in part of the genome, but this observation requires genetic markers that have been mapped. Sequencing is a third way in which inversions are detected. The short reads that are characteristic of current high-throughput sequencing methods are well-suited to determine if an individual carries an inversion that has already been characterized by its breakpoints, but this technology is poor at prospecting for new inversions. In many cases, there is virtually no difference in the genetic content of inverted and uninverted chromosomes—only the linear order of DNA bases is changed. This situation presents evolutionary biologists with an intriguing question: if an inverted chromosome has (almost) the same genetic information as an uninverted one, what could cause it to spread through a population? This primer begins with an overview of the evolutionary forces that act on inversions. It then discusses the importance of inversions to the evolution of sex chromosomes, speciation, and local adaptation. Finally, we will see how several of these themes are illuminated by an exciting study on an inversion in a plant that appears in this issue of PLoS Biology.