Image restoration is a long-standing problem in low-level computer vision with many interesting applications. An effective framework for image restoration is to make use of the variational model. Traditional variational models aim at solving a minimization problem using some iterative optimization algorithms which may be relatively time-consuming and therefore challenging for practical applications. Recently, several approaches have been proposed to solve this deficiency. These approaches do not exactly solve the minimization problem anymore, but in contrast, they run the solving optimization algorithm for several steps, and each iterative step is optimized by training. In this presentation, the basic idea of these approaches and their relationship with Recurrent Neural Networks are briefly reviewed. Besides, we also introduce our recent works in this domain.