Index of refraction, a fundamental optical constant that enters in the descriptions of almost all optical phenomena, has long been considered an intrinsic property of a material. However, the recent progress in negative-index material (NIM) research has shown that the utilization of deep-subwavelength-scale features can provide a means to engineer fundamental optical constants such as permittivity, permeability, impedance, and index of refraction. Armed with new nanofabrication techniques, researchers worldwide have developed and demonstrated a variety of NIMs. One implementation uses a combination of electric and magnetic resonators that simultaneously produce negative permittivity and permeability, and consequently negative refractive index. Others involve chirality, anisotropy, or Bragg resonance in periodic structures. NIM research is the beginning of new optical materials research in which the desired optical properties and functionalities are artificially generated. Clearly, creating negative index materials is not the only possibility, and the most recent developments explore new realms of materials with near-zero indexes and inhomogeneous index profiles that can produce novel phenomena such as invisibility. Furthermore, the concept of controlling macroscopic material properties with a composite structure containing subwavelength-scale features extends to the development of acoustic metamaterials. By providing a review of recent progress in NIM research, we hope to share the excitement of the field with the broader materials research community and also to spur new ideas and research directions.