A bistable chain/lattice is an assembly of masses joined by bistable springs; it describes the reversible or irreversible transition of material properties. We model the force in a spring as a discontinuous piecewise linear function of its elongation (short and long modes). The state of minimal energy of the mass-spring chain of such springs (Maxwell law) is characterized by a transition from one phase to another at the critical elongation of the springs; the homogenized potential energy is the convex envelope of the nonconvex energy of the springs. The minimal energy of triangular lattices from such springs is characterized by a quasi-convex hull comprising equally elongated compatible networks of long and short springs. The compatibility conditions restrict the patterns of long and short springs. The chain dynamics becomes a sequence of linear system solutions perturbed by instant impacts that model the transition of springs. With additional assumptions of the regularity of these impacts, one can explicitly describe waves of transition. The long-term behavior of a bistable chain is viewed as a stochastic process; in this case, the Central Limit theorem allows for finding the homogenized force-vs-elongation dependence and nonlinear stiffness of the whole chain. Depending on the kinetic energy of vibrations, it varies between Maxwell's rule and the linearized spring stiffness. The long-term state of the vibrating stretched lattice shows patterns of long and short links that minimize the energy. We describe the long-time behavior of the entire system as a nonlinear homogenized stress-strain relation between its average deformation and externally applied forces; it parametrically depends on the initial kinetic energy in the system. The paper summarizes the collaborative work with Leonid Slepyan, Alexander Balk, Elena Cherkaev, Seubpong Leelavanichkul, Alexander Panchenko, Michael Ryvkin, Andrejs Treibergs, Predrag Krolika, Charlotte Blake, Debdeep Bhattacharya, and Tyler Evans.