Data-driven discovery of the governing equations describing the dynamics of physical systems has long been a cornerstone of scientific advancement, dating back to Kepler's laws of planetary motion derived from Tycho Brahe's astronomical observations. Today, the significant high-dimensionality and complexity of datasets make it impossible for the human brain to perform similar analyses unaided. This challenge has catalyzed the rise of machine learning (ML), which transforms large and complex data from simulations and/or experiments into useful and explainable science, hence, augmenting the domain knowledge. ML-enabled/enhanced modeling has demonstrated strong promise in revolutionizing scientific computing for real-world complex engineering systems, yielding unique opportunities to examine the operation of the technologies in detail as well as to automate their optimization and control. In recent years, ML applications have surged across various scientific domains, with a particularly promising area being the discovery of dynamics in complex physical systems where the governing equations may be fully or partially unknown. In this paper, we aim to present an overview of this ML application, highlighting its importance for the advancement of plasma science and technology. We demonstrate the capabilities of a novel in-house developed data-driven algorithm, Phi Method, for dynamics discovery and identifying closure terms for plasma fluid systems of equations. The focus will be on learning the parametric dynamics of a plasma configuration using Phi Method, showcasing that the learned dynamics exhibits remarkable generalizability across the parameter space, even in extrapolation scenarios.