Many of the most commonly cited examples of exquisite adaptation are of coevolved symbioses. As we learn more about the coevolutionary process, however, it is becoming increasingly evident that coevolution may also keep populations moderately maladapted much of the time. As a result, coevolving populations may only rarely occupy adaptive peaks, because the selective landscape is under continual change through reciprocal selection on the species themselves. These shifting patterns of coadaptation are further shaped by the geographic structure of most species. Selection mosaics across landscapes and coevolutionary hotspots can favor different evolutionary trajectories in different populations. The combined action of gene flow, random genetic drift, and local extinction of populations may then continually remold these local patterns, creating a geographic mosaic in the degrees of maladaptation found within local interactions. Recent mathematical models of the geographic mosaic of coevolution suggest that complex mosaics of maladaptation are a likely consequence of spatially structured species interactions. These models indicate that the spatial structure of maladaptation may depend upon the type of coevolutionary interaction, the underlying selection mosaic, and patterns of gene flow across landscapes. By maintaining local polymorphisms and driving the divergence of populations, coevolution may produce spatial patterns of maladaptation that are a source of ongoing innovation and diversification in species interactions.