This paper reviews proximal splitting methods in signal processing, focusing on their application to convex optimization problems. Proximity operators, which generalize projection operators, are central to these methods. They allow for the efficient solution of problems involving the sum of multiple convex functions, including those that are non-differentiable. The paper discusses various proximal algorithms, such as the forward-backward and Douglas-Rachford algorithms, which provide a unified framework for solving a wide range of signal processing tasks. These methods are particularly effective for problems involving sparsity, denoising, and restoration. The paper also addresses composite problems with linear transformations and presents parallel variants of these algorithms for handling multiple functions. Key applications include image and signal recovery, where proximal methods enable the solution of problems with complex constraints and objectives. The paper emphasizes the flexibility and power of proximal methods, showing how they can be applied to a broad spectrum of signal processing challenges, from restoration and reconstruction to synthesis and design. The convergence properties of these algorithms are analyzed, and their practical implementation is discussed, highlighting their efficiency and robustness in handling non-smooth and large-scale optimization problems.This paper reviews proximal splitting methods in signal processing, focusing on their application to convex optimization problems. Proximity operators, which generalize projection operators, are central to these methods. They allow for the efficient solution of problems involving the sum of multiple convex functions, including those that are non-differentiable. The paper discusses various proximal algorithms, such as the forward-backward and Douglas-Rachford algorithms, which provide a unified framework for solving a wide range of signal processing tasks. These methods are particularly effective for problems involving sparsity, denoising, and restoration. The paper also addresses composite problems with linear transformations and presents parallel variants of these algorithms for handling multiple functions. Key applications include image and signal recovery, where proximal methods enable the solution of problems with complex constraints and objectives. The paper emphasizes the flexibility and power of proximal methods, showing how they can be applied to a broad spectrum of signal processing challenges, from restoration and reconstruction to synthesis and design. The convergence properties of these algorithms are analyzed, and their practical implementation is discussed, highlighting their efficiency and robustness in handling non-smooth and large-scale optimization problems.