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Interfaces between media with infinite anisotropy, defined by infinite permittivity or permeability in one direction, offer new opportunities for controlling and manipulating light at the nanoscale. Reflectionless, diffraction‐free routing of deep‐subwavelength optical beams and images using interfaces between infinitely anisotropic media are demonstrated. It is shown how to achieve extremely large anisotropy using metamaterial designs that can be implemented with existing materials.