Topological Data Analysis (TDA) is an emerging field that bridges topology, applied mathematics, and data science, offering powerful tools to analyze and model complex systems. TDA focuses on understanding the “shape” of high-dimensional data, particularly in cases where conventional methods struggle to capture underlying structures. This review explores the theoretical foundations of TDA, its mathematical framework, and its application to complex systems modeling in fields like biology, neuroscience, and finance. A detailed discussion on Persistent Homology, computational algorithms, mathematical models, and practical challenges is also presented, showcasing how TDA provides new insights into high-dimensional data.