Simulations are widely categorized into distinct methodological types based on how they model real-world systems, behaviors, and variables. The first major type is discrete-event simulation, which models systems as a discrete sequence of events in time, commonly used in manufacturing, logistics, and supply chain management to analyze bottlenecks. The second type is continuous simulation, which uses differential equations to represent systems where state variables change continuously over time, frequently applied in physics, aerospace engineering, and chemical processing. The third type is Monte Carlo simulation, a probabilistic approach that uses repeated random sampling to calculate numerical outcomes and account for risk and uncertainty in financial forecasting and project management. The fourth type is agent-based simulation, which models the simultaneous interactions of autonomous individual entities or agents to observe emergent collective behavior in complex social, biological, or economic systems. Each of these four foundational simulation paradigms offers unique mathematical frameworks designed to solve specific operational, predictive, and analytical challenges across diverse industries.