Plug-and-play methods constitute a class of iterative algorithms for imaging inverse problems where regularization is performed by an off-the-shelf Gaussian denoiser. These methods have demonstrated impressive visual results, particularly when the denoiser is parameterized by deep neural networks. However, the theoretical convergence of PnP methods has yet to be fully established. This talk begins with an overview of the literature on PnP algorithms, followed by the introduction of new convergence results for these methods when paired with specific denoisers, known as Gradient-Step and Proximal denoisers. Finally, in order to address images corrupted by Poisson noise, we will introduce a novel Bregman version of Plug-and-Play algorithms and its associated convergence analysis.