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Flow chemistry has emerged as a transformative methodology in chemical research, enabling precise control over reaction parameters, enhanced safety, and scalability compared to traditional batch processes. When integrated with automation and real-time analytics, flow chemistry forms the backbone of self-optimizing and self-driving laboratories. Recent advances include high-throughput experimentation (HTE), Bayesian-optimized flow systems with inline spectroscopic feedback, modular platforms for multistep synthesis, and integration with artificial intelligence (AI) and machine learning (ML). Applications span photochemistry, catalysis, polymer synthesis, peptide chemistry, and biomedicine. This paper surveys the theoretical foundations, technological platforms, and key applications of flow chemistry in automated experimentation. It also explores challenges- including data integration, cost, and non-standardization- and considers future directions in autonomous discovery, sustainable chemistry, and industrial adoption.