This paper provides a comprehensive review of Limit Order Book (LOB) simulation models, which are essential for developing and calibrating automated trading strategies in algorithmic trading. The authors classify existing models based on their methodological approaches, such as agent-based simulations, stochastic processes, and modern AI techniques, highlighting how advancements in computing power and AI have enriched these simulations. Additionally, the review aggregates the stylized facts commonly used in literature to test model accuracy, ensuring that simulations reflect real market behaviors.

A key focus of the paper is on modeling price impact, a critical phenomenon in algorithmic trading that affects strategy performance. The authors conduct a comparative analysis of various models, evaluating their quality of fit against empirical data to assess how well they replicate market dynamics. This analysis reveals differences in model performance, providing insights for researchers and practitioners in selecting or developing more effective LOB simulations. The review serves as a valuable resource for understanding the state of the art in LOB modeling and its applications in financial markets.