The field of metamaterials has opened landscapes of possibilities in basic science, and a paradigm shift in the way we think about and design emergent material properties. In many scenarios, metamaterial concepts have helped overcome long-held scientific challenges, such as the absence of optical magnetism and the limits imposed by diffraction in optical imaging. As the potential of metamaterials, as well as their limitations, become clearer, these advances in basic science have started to make an impact on several applications in different areas, with far-reaching implications for many scientific and engineering fields. At optical frequencies, the alliance of metamaterials with the fields of plasmonics and nanophotonics can further advance the possibility of controlling light propagation, radiation, localization and scattering in unprecedented ways. In this review article, we discuss the recent progress in the field of metamaterials, with particular focus on how fundamental advances in this field are enabling a new generation of metamaterial, plasmonic and nanophotonic devices. Relevant examples include optical nanocircuits and nanoantennas, invisibility cloaks, superscatterers and superabsorbers, metasurfaces for wavefront shaping and wave-based analog computing, as well as active, nonreciprocal and topological devices. Throughout the paper, we highlight the fundamental limitations and practical challenges associated with the realization of advanced functionalities, and we suggest potential directions to go beyond these limits. Over the next few years, as new scientific breakthroughs are translated into technological advances, the fields of metamaterials, plasmonics and nanophotonics are expected to have a broad impact on a variety of applications in areas of scientific, industrial and societal significance.