Fluid bridges are ubiquitous soft structures of finite size that conform to and link the surfaces of neighboring objects. Fluid joints, the specific type of fluid bridge with at least one extremity constrained laterally, display even more pronounced reactivity and self-restoration, which make them remarkably suited for assembly, actuation, and manipulation purposes. Their peculiar surface and bulk properties place fluid joints at the rich intersection of diverse scientific interests, and foster their widespread use throughout micro- and nanotechnology. A critical survey of the mechanics and of the manifold applications of fluid bridges and joints in micro- and nanosystems is presented here, along with current challenges and multidisciplinary perspectives.