Starting with an introduction to variational/PDE based image processing, this talk will focus on new developments of fast algorithms for higher order variational imaging models.  For example, recent developments of fast algorithms, based on operator splitting, augmented Lagrangian, and alternating minimization, enabled us to revisit some of the variational image models, such as Euler’s Elastica image inpainting model.  Main ideas of the models and algorithms, some analysis and numerical results will be presented.