Researchers have developed variable-impedance mechanisms to control the dynamic response of robotic systems and improve their adaptivity, robustness, and efficiency. However, these mechanisms have limitations in size, cost, and convenience, particularly for variable damping. We demonstrate that laminar jamming structures can transform the dynamic response of robotic structures and systems while overcoming these limitations. In laminar jamming, an external pressure gradient is applied to a laminate of compliant material, changing its stiffness and damping. In this latter, we combine analysis, simulation, and characterization to formulate a lumped-parameter model that captures the nonlinear mechanical behavior of jamming structures and can be used to rapidly simulate their dynamic response. We illustrate that by adjusting the vacuum pressure, the fundamental features of the dynamic response (i.e., frequency, amplitude, decay rate, and steady-state value) can be tuned on command. Finally, we demonstrate that jamming structures can be integrated into soft structures and traditional rigid robots to considerably alter their response to impacts. With the models and demonstrations provided here, researchers may move further toward building versatile and transformative robots.