Leaky waves have been among the most active areas of research in microwave engineering over the second half of the 20th century. They have been shown to dominate the near-field of several open wave-guiding structures, of great interest to tailor their radiation, guidance and filtering properties. The elegant theoretical analyses and deep physical in-sights in this area, developed in an era in which computational resources were limited, represent a fundamental scientific legacy that is still extremely relevant in today's engineering society and beyond. In this regard, the relevance of leaky-wave concepts has been increasingly recognized in recent times over a broader scientific community, including optics and physics societies. In this paper, after revisiting the fundamental concepts of leaky-wave theory, we discuss and connect different relevant research activities in which leaky-wave concepts have been applied, with the goal of facilitating multidisciplinary interactions on these topics. In addition to the canonical microwave applications of leaky waves, particular attention is devoted to a few areas of interest in modern optics, such as directive optical antennas, extraordinary optical transmission, and embedded scattering eigenvalues, in which leaky waves play a fundamental role.