This paper explores the application of optimization techniques in fluid dynamics, focusing on mathematical modeling, numerical simulations, and practical case studies. We begin by providing a comprehensive overview of optimization methods in fluid dynamics, covering gradient-based optimization, adjoint methods, control theory approaches, and machine learning techniques. Subsequently, we delve into three key application areas: aerodynamic shape optimization, flow control in pipelines, and environmental fluid dynamics. Through detailed case studies, we demonstrate the effectiveness of optimization algorithms in improving system performance and efficiency. In aerodynamic shape optimization, we minimize drag while maintaining lift, showcasing the power of gradient-based optimization and adjoint methods. In flow control, we optimize inlet velocity profiles to minimize energy loss and ensure specified flow rates, employing linear quadratic regulator (LQR) techniques. Finally, in environmental fluid dynamics, we address pollutant dispersion in rivers by optimizing flow rates from upstream sources to minimize downstream pollution concentration, using model predictive control (MPC) methods. Our study contributes practical insights into the integration of optimization techniques with fluid dynamics, offering guidance for researchers and practitioners in tackling real-world engineering challenges.