yberphysical systems (CPSs) are expected to operate in safety-critical scenarios, and are increasingly getting distributed and physically separated. CPSs are characterized by complex dynamical behavior arising from emergent inter-agent interactions, having discrete logic-based programs, data-driven methods employed in-the-loop, or by simply having highly nonlinear dynamics. Despite this, safety and security properties for CPSs need to be computed, often in real-time over analytically accurate solutions of the associated high dimensional partial differential equations (PDEs). In this dissertation, we investigate numerical approximation schemes to compute safety properties (or reachable sets) for CPSs with differing natures of complexities, without solving the associated PDEs. We solve for reachable sets for unknown dynamical systems with polynomial approximations. Similar approximation schemes can be extended to multi-agent systems and dynamical systems with neural-networks-in-the-loop. Such systems are increasingly applicable in real life instances, such as internet of things, urban air mobility, and data-driven controllers in-the-loop. We utilize the system's trajectory data to compute equivalent system models, and utilize the data-driven models to find approximate reachable sets using polytopic or interval approximations, thereby side stepping PDE solutions. We also investigate cyberphysical vulnerabilities in CPSs from emergent multi-agent behavior, and single agent interacting with multiple controllers via supervisory cyber layers. Each problem is accompanied with associated illustrative examples and numerical simulations. Finally, we present an extensive discussion of possible directions for future work, both, that result directly from the works presented in this dissertation, and those that stem from the assumptions that can be handled immediately.