Deep reinforcement learning (DRL) has recently been adopted in a wide range of physics and engineering domains for its ability to solve decisionmaking problems that were previously out of reach due to a combination of non-linearity and high dimensionality. In the last few years, it has spread in the field of computational mechanics, and particularly in fluid dynamics, with recent applications in flow control and shape optimization. In this work, we conduct a detailed review of existing DRL applications to fluid mechanics problems. In addition, we present recent results that further illustrate the potential of DRL in Fluid Mechanics. The coupling methods used in each case are covered, detailing their advantages and limitations. Our review also focuses on the comparison with classical methods for optimal control and optimization. Finally, several test cases