Compliant mechanisms have gained increasing attention in robotics, enabling applications ranging from soft manipulators to precision positioning stages. Compared to conventional mechanisms, they offer backlash- and friction-free operation while reducing part count and assembly complexity. Among these, planar strip-based structures—such as cross-strip pivots and parallelogram flexures—are widely used to approximate rotational and prismatic joints, respectively. Despite their widespread adoption, such mechanisms typically exhibit monotonic stiffness characteristics and are primarily designed to enforce kinematic constraints, limiting their functional versatility. In this work, we extend the design space and explore the application scope of planar strip- based compliant mechanisms by introducing buckled elastic strip structures (BESTs). By incorporating controlled buckling into strip elements, BESTs enable highly non-linear stiffness characteristics, allowing complex mechanical behavior to be encoded through tailored elastic energy landscapes. We present and experimentally validate a modeling and design framework based on elliptic integral solutions to the Euler elastica equations. These properties enable key aspects of mechanical intelligence, including multistability for reconfigurability, hysteretic stiffness for full gait-cycle generation in walking robots from a simple back-and-forth actuation, elastic energy storage for jumping, and variable stiffness for adaptive robotic structures. We demonstrate these capabilities through multiple systems built from BESTs, such as a passively reconfigurable quadcopter designed for gap traversal.