Transformation optics is an emerging technique for the design of advanced electromagnetic media. Transformation optical devices exploit the form invariance of Maxwell's equations, allowing geometry to play the dominant role in the design process rather than traditional wave or ray optics. The use of coordinate transformations vastly eases the burden of design for a large class of devices, though at the expense of increasing the complexity of the underlying materials used. Although the required constitutive parameters of a transformation optical structure can be challenging—inherently anisotropic and spatially varying, with both magnetic and electric response—nevertheless the parameter requirements can often be met or approximated through the use of artificially structured metamaterials. Here, we review the basic concepts associated with transformation optics and provide several examples to illustrate its application.