Machine learning is transforming fluid mechanics by enabling data-driven modeling, optimization, and control. This review outlines the historical development, current applications, and future opportunities of machine learning in fluid mechanics. Fluid mechanics has long relied on domain expertise, statistical analysis, and heuristic algorithms to analyze data from experiments, field measurements, and simulations. However, the increasing volume of data, combined with advances in computational power and algorithms, has created a new paradigm where machine learning can extract insights and automate tasks in fluid mechanics. Machine learning algorithms, including supervised, unsupervised, and semi-supervised learning, are being applied to fluid mechanics for tasks such as flow modeling, optimization, and control. These algorithms provide a modular and flexible framework for addressing challenges in fluid mechanics, such as reduced-order modeling, experimental data processing, shape optimization, turbulence closure, and control. The strengths and limitations of these methods are discussed in the context of scientific inquiry that integrates data into modeling, experimentation, and simulation. The review highlights the importance of understanding how learning algorithms work and when they succeed or fail. It emphasizes the need to balance excitement about machine learning capabilities with the reality that its application to fluid mechanics is an open and challenging field. The integration of domain knowledge into learning algorithms is also discussed, as it can enhance the performance and interpretability of machine learning models. The review also addresses the challenges and opportunities for machine learning in fluid dynamics. Fluid dynamics presents unique challenges, such as the need to precisely quantify physical mechanisms, the complexity of multi-scale phenomena, and the computational demands of simulations. Machine learning can help overcome these challenges by providing efficient and accurate models for flow prediction and control. However, interpretability, generalizability, and the ability to provide guarantees on performance remain critical issues in the application of machine learning to fluid mechanics. The review concludes that the confluence of first principles and data-driven approaches in fluid mechanics has the potential to transform both the field and machine learning. This review provides a comprehensive overview of the current state of machine learning in fluid mechanics, highlighting its potential to advance both scientific understanding and engineering applications.Machine learning is transforming fluid mechanics by enabling data-driven modeling, optimization, and control. This review outlines the historical development, current applications, and future opportunities of machine learning in fluid mechanics. Fluid mechanics has long relied on domain expertise, statistical analysis, and heuristic algorithms to analyze data from experiments, field measurements, and simulations. However, the increasing volume of data, combined with advances in computational power and algorithms, has created a new paradigm where machine learning can extract insights and automate tasks in fluid mechanics. Machine learning algorithms, including supervised, unsupervised, and semi-supervised learning, are being applied to fluid mechanics for tasks such as flow modeling, optimization, and control. These algorithms provide a modular and flexible framework for addressing challenges in fluid mechanics, such as reduced-order modeling, experimental data processing, shape optimization, turbulence closure, and control. The strengths and limitations of these methods are discussed in the context of scientific inquiry that integrates data into modeling, experimentation, and simulation. The review highlights the importance of understanding how learning algorithms work and when they succeed or fail. It emphasizes the need to balance excitement about machine learning capabilities with the reality that its application to fluid mechanics is an open and challenging field. The integration of domain knowledge into learning algorithms is also discussed, as it can enhance the performance and interpretability of machine learning models. The review also addresses the challenges and opportunities for machine learning in fluid dynamics. Fluid dynamics presents unique challenges, such as the need to precisely quantify physical mechanisms, the complexity of multi-scale phenomena, and the computational demands of simulations. Machine learning can help overcome these challenges by providing efficient and accurate models for flow prediction and control. However, interpretability, generalizability, and the ability to provide guarantees on performance remain critical issues in the application of machine learning to fluid mechanics. The review concludes that the confluence of first principles and data-driven approaches in fluid mechanics has the potential to transform both the field and machine learning. This review provides a comprehensive overview of the current state of machine learning in fluid mechanics, highlighting its potential to advance both scientific understanding and engineering applications.