Mechanical metamaterials are artificially designed structures that exhibit unique properties due totheir internal structure rather than their composition, e.g., negative Poisson’s ratio, tunable stiff- ness, and advanced thermal characteristics. While the static properties of mechanical metamaterials have been widely studied, their nonlinear dynamics remain largely unexplored, which could pave ways for innovative design and optimization for novel applications related to deployable structures, reconfigurable robots, and more. This dissertation aims to expand the fundamental understanding of flexible mechanical metamaterials through the combination of analytical, numerical, and experimental methods. This thesis is divided into three areas: the triggering of phase transitions through the collision of vector solitons in a multistable structure comprising rotating squares, the exploration of asymptotic energy propagation in a flexible Kagome lattices, and the development of a bio-inspired pulse-driven flexible platform for rapid motion control of underactuated systems. These studies demonstrate that mechanical metamaterials possess rich nonlinear dynamical behaviors, including soliton collisions leading to phase transitions, the preservation and disruption of topological modes under nonlinear loading, and spatiotemporal dynamics that can be applied toward stabilization of robots subjected to sudden loads.