Active structures have the ability to change their shape, properties, and functionality as a response to changing operational conditions, which makes them more versatile than their static counterparts. Despite recent advances in engineering, materials science, and fabrication processes, the systematic design and fabrication of active structures is still a challenge as many structures are designed by hand in a trial and error process and thus limited by engineers' knowledge and experience. This thesis aims to systematically design, fabricate, and test novel and active structures that can change their shape and mechanical properties. The structures overcome known limitations such as the reversibility of deformations triggered by one-way active materials and transforming into multiple states and shapes. This is achieved by combining mechanical principles, material knowledge, multi-material 3D printing, and computational design methods. First, fundamental properties of lattice mechanics are exploited to design structures at the verge of determinacy. By tailoring the topology and geometry of structures, kinematic deformation modes with a specified target shape and a single degree of freedom can be directly integrated. These shape morphing deformations are, by design, reversible and can feature multiple, independent deformation modes for different input displacements. The concept of determinacy is further used to design structures that can switch between both extremes of cellular structures, bending-dominated and stretch dominated behavior, in a single structure. This is achieved by combining a distinct topological and geometric design with a 3D-printed, heat-responsive shape-memory polymer (SMP), which enables topology transformation and provides direct control over the mechanical properties of the structures. To overcome the tedious programming step and one-way actuation of many SMPs and make active shape-morphing deformations reversible, the combination of two different 3D-printed SMPs in a single structure is explored to encode shape-morphing behavior under global heating and a single input actuation. By design, the structures can have two different, mechanically stable states, where the topology remains intact. To achieve multiple target states with a single structure and only one input actuation, local heating is explored in the final part of this thesis. Along with a novel topology optimization approach that ensures fabricability of the structures and compatibility with the drop-in, copper coil heating elements, different target states for a single input actuation are encoded in the structure. A material dithering scheme based on multi-material 3D printing and sequential heating are used to control the thermo-mechanical properties of the structures and switch between the different deformation modes. While some of the proposed concepts are limited by current 3D printing processes, the generality of both the underlying principles and the computational methods makes them directly applicable to future advances in materials science and fabrication technologies. As such, the findings in this thesis provide a first step towards the integrated design and fabrication of active structures and the development towards industrial applications across many length scales and fields such as the shape-morphing wings of aircraft, car panels, and building facades.