The tight interaction between information technology and the physical world inherent in Cyber-Physical Systems (CPS) can challenge traditional approaches for monitoring safety and security. Data collected for robust CPS monitoring is often sparse and may lack rich training data describing critical events/attacks. Moreover, CPS often operate in diverse environments that can have significant inter/intra-system variability. Furthermore, CPS monitors that are not robust to data sparsity and inter/intra-system variability may result in inconsistent performance and may not be trusted for monitoring safety and security. Towards overcoming these challenges, this paper presents recent work on the design of parameter-invariant (PAIN) monitors for CPS. PAIN monitors are designed such that unknown events and system variability minimally affect the monitor performance. This work describes how PAIN designs can achieve a constant false alarm rate (CFAR) in the presence of data sparsity and intra/inter system variance in real-world CPS. To demonstrate the design of PAIN monitors for safety monitoring in CPS with different types of dynamics, we consider systems with networked dynamics, linear-time invariant dynamics, and hybrid dynamics that are discussed through case studies for building actuator fault detection, meal detection in type I diabetes, and detecting hypoxia caused by pulmonary shunts in infants. In all applications, the PAIN monitor is shown to have (significantly) less variance in monitoring performance and (often) outperforms other competing approaches in the literature. Finally, an initial application of PAIN monitoring for CPS security is presented along with challenges and research directions for future security monitoring deployments.