Reconfigurable three-dimensional (3D) structures that can reversibly change their geometries and thereby their functionalities are promising for a wide range of applications. Despite intensive studies, the lack of fundamental understanding of the highly nonlinear multistable states existing in these structures has significantly hindered the development of reconfigurable systems that can realize rapid, well-controlled shape change. Herein we present a systematic, integrated experimental and computational study to control and tailor the multistable states of 3D structures and their reconfiguration paths. Our energy landscape analysis using a discrete shell model and minimum energy pathway methods leads to design maps for a controlled number of stable states by varying geometry and material parameters, and energy-efficient reconfiguration paths among the multistable states. Concurrently, our experiments show that 3D structures assembled from ferromagnetic composite thin films of diverse geometries can be rapidly reconfigured among their multistable states, with the number of stable states and reconfigurable paths in excellent agreement with computational predictions. In addition, we demonstrate a wide breadth of applications including reconfigurable 3D light emitting systems, remotely- controlled release of particles/drugs from a reconfigurable structure, and 3D structure arrays that can form desired patterns following the written path of a magnetic “pen”. Our results represent a critical step towards the rational design and development of well-controlled, rapidly and remotely reconfigurable structures for many applications.