Under-deck, cable-stayed bridges and combined cable-stayed bridges constitute two innovative bridge types that have been designed and built on relatively few occasions over the last 30 years, in most cases by renowned structural engineers, such as Leonhardt, Schlaich, Virlogeux, Manterola, Robertson and Cremer. In these bridge types, the stay cables have unconventional layouts: either below the deck, in the case of under-deck cable-stayed bridges, or above and below the deck, in the case of combined cable-stayed bridges. In this paper, a general and critical overview of the current state-of-the-art is outlined, addressing issues related to proposals, built bridges and research. Significant attention is paid to their highly efficient structural behaviour and unconventional design criteria, both of which lead to a significant reduction in the amount of required materials, in comparison with conventional bridges without stay cables, and thus allow for sustainable design. Other advantages of these bridges, such as multiple construction possibilities, strong aesthetic characteristics and their broad range of potential applications, are also stressed.