Digital images are often corrupted by noise mixtures than can be modeled as combinations of Gaussian and Poisson distributions, which are usually generated by the acquisition devices. Various effective mixed Poisson-Gaussian noise filtering approaches have been developed in the last years. Those state of the art mixed noise removal techniques that use nonlinear partial differential equation (PDE) based models are surveyed here. Our own contributions in this image restoration domain are also described in this work. Several PDE variational models for mixed Poisson-Gaussian noise reduction, which use the total variation regularization, are presented first. Some of them combine the TV - ROF Denoising model that removes the Gaussian noise to modified TV schemes, adapted for the Poisson noise. Other variational mixed noise removal solutions are based on spatially adaptive total variation regularization terms. A fast total variation-based algorithm for image restoration with exact Poisson–Gaussian likelihood is also disscused in this work. Another variational Poisson-Gaussian denoising technique presented here uses a functional combining the TV regularisation, Kullback-–Leibler divergence and the L2 norm. Then, second-order total generalized variation (TGV) regularized mixed noise removal models are described. These variational denoising techniques lead to some nonlinear PDE models that are next discretized by applying some finite differencebased numerical algorithms. Then, several PDE-based restoration approaches dealing with this noise mixture and proposed by us are described here. Besides a variational Poisson-Gaussian noise reduction method, we have also developed some non-variational mixed noise removal techniques based on well-posed PDE models. One of them uses a parabolic nonlinear fourth-order PDE model, while another method presented here is based on a second-order hyperbolic PDE model. Method comparison results illustrating their effectiveness are also provided.