Advances in Scientific Machine Learning (SciML) are poised to have profound impact within engineering domains that deal with industrial control and process systems (ICPS). Such systems are characterized by the operation of interconnected physical equipment; complex control and data acquisition systems; and sensor data that is nonlinear, noisy, and multi-dimensional. Consequently, maintaining reliable and predictable operation of an ICPS is challenging and often relies on robust advisory systems and expert operator decisions. SciML methods thus offer unique opportunities to develop new emulation and analysis tools that can ultimately enhance and redefine ICPS operation and decision making activities. This talk presents our SciML developments and experiences in using data-driven surrogates and causal discovery methods within the ICPS paradigm. We first discuss perspectives on the use of dynamic surrogate architectures to develop real-time ICPS emulators and how they facilitate effective simulation life-cycle development versus traditional emulator approaches. We further demonstrate how dynamic surrogate models naturally enable state-of-the-art numerical optimization and model predictive control capabilities. Next, we present challenges and opportunities toward utilizing causal discovery methods in the context of monitoring and fault analysis. We discuss how causal discovery methods provide a natural framework to both assist operators in understanding complex system behavior and to help diagnose root causes of faults without requiring a pre-existing historian of faulty operating conditions. We lastly use a benchmark chemical process dataset (the Tennessee Eastman Process) to demonstrate our results.