Strong adherence to underwater or wet surfaces for applications like tissue adhesion and underwater robotics is a significant challenge. This is especially apparent when switchable adhesion is required that demands rapid attachment, high adhesive capacity, and easy release. Nature displays a spectrum of permanent to reversible attachment from organisms ranging from the mussel to the octopus, providing inspiration for underwater adhesion design that has yet to be fully leveraged in synthetic systems. Here, we review the challenges and opportunities for creating underwater adhesives with a pathway to switchability. We discuss key material, geometric, modeling, and design tools necessary to achieve underwater adhesion similar to the adhesion control demonstrated in nature. Through these interdisciplinary efforts we envision that bioinspired adhesives can rise to or even surpass the extraordinary capabilities found in biological systems.