Conventionally, static and dynamic instabilities should be avoided in design, since buckling leads typically to damage or even collapse. However, recent years have observed a growing interest in bistable and multistable structures, which can assume different stable positions without damage. Their range of application include mainly vibration control, energy absorbers, signal processing, energy harvesting, microelectromechanical systems (MEMS), robotics, deployable structures, morphing structures and programmable devices as well as metamaterials. Here a review of the subject is presented, with emphasis on recent review articles where the reader can find an encompassing view of this research area. In many applications, multistable behavior is accomplished by coupling unidimensional bistable elements, such as shallow arches and von Mises trusses, which present individually two stable and one unstable equilibrium states. Shell-like structures, particularly those of composite materials, may also display a high degree of multistability. In spite of the increasing number of publications on multistable systems, few detailed static and dynamic nonlinear analyses of these systems, clarifying their equilibrium paths and stability, bifurcations and coexisting static and dynamic solutions can be found in literature. However, such type of analysis is essential not only in understanding their complex nonlinear behavior but also to serve as a guide to experiments and practical applications. Numerical tools for elastic stability and nonlinear vibration analysis are reviewed in this chapter and their use in multistable analysis are underlined and illustrated using the results of simple models composed by two shallow von Mises trusses connected by rigid and soft elements.