Grain growth in metals and alloys is a critical phenomenon that influences materials' mechanical properties and performance. Understanding and predicting grain evolution during thermo-mechanical treatments are vital for optimizing material processing and designing improved materials. In this report, we conduct a detailed review of the Phase-Field Method and compare it with two other prominent computational techniques, Monte Carlo and Cellular Automata, commonly used to model grain growth during thermo-mechanical treatments. The Phase-Field Method is a powerful computational technique for simulating microstructural evolution. This review provides an in-depth analysis of the underlying mechanisms, influential factors, and the impact of thermo-mechanical conditions on grain growth kinetics. The insights from recent research papers, simulations, and experimental studies shed light on the practical implications for materials engineering and manufacturing processes.