Organic synthesis is fundamental to drug research and development, providing the means to design and create novel molecules. Retrosynthetic analysis, a core technique in organic chemistry, involves deconstructing a target molecule into simpler precursor compounds. This approach encompasses two primary tasks: single-step retrosynthetic prediction, which identifies reactants for a specific product, and multi-step retrosynthetic prediction, which optimizes complete synthetic pathways. Traditional retrosynthesis, rooted in expert knowledge and heuristic rules, has been transformed by advancements in machine learning, large-scale reaction databases, and computational chemistry. Template-based methods utilize predefined reaction templates to guide predictions, while template-free approaches, including sequence-based and graph-based models, employ machine learning techniques such as machine translation to uncover novel reaction patterns. For multi-step retrosynthesis, algorithms like Monte Carlo tree search, beam search, and A* search efficiently explore and identify optimal synthetic routes. These computational methods enhance the scalability and accuracy of retrosynthetic planning, making them invaluable tools in drug discovery. As data-driven retrosynthesis continues to evolve, it holds the potential to significantly accelerate and refine the process of organic synthesis, driving innovation in pharmaceutical research.