This paper describes the fabrication of 3D soft, inflatable structures from thin, 2D tiles fabricated from elastomeric polymers. The tiles are connected using soft joints that increase the surface area available for gluing them together, and mechanically reinforce the structures to withstand the tensile forces associated with pneumatic actuation. The ability of the elastomeric polymer to withstand large deformations without failure makes it possible to explore and implement new joint designs, for example "double-taper dovetail joints,"that cannot be used with hard materials. This approach simplifies the fabrication of soft structures comprising materials with different physical properties (e.g., stiffness, electrical conductivity, optical transparency), and provides the methods required to "program" the response of these structures to mechanical (e.g., pneumatic pressurization) and other physical (e.g., electrical) stimuli. The flexibility and modularity of this approach is demonstrated in a set of soft structures that expanded or buckled into distinct, predictable shapes when inflated or deflated. These structures combine easily to form extended systems with motions dependent on the configurations of the selected components, and, when fabricated with electrically conductive tiles, electronic circuits with pneumatically active elements. This approach to the fabrication of hollow, 3D structures provides routes to new soft actuators.