Super resolution problems are widely discussed in medical imaging. Spatial resolution of medical images are not sufficient due to the constraints such as image acquisition time, low irradiation dose or hardware limits. To address these problems, different super resolution methods have been proposed, such as optimization or learning-based approaches. Recently, deep learning methods become a thriving technology and are developing at an exponential speed. We think it is necessary to write a review to present the current situation of deep learning in medical imaging super resolution. In this paper, we first briefly introduce deep learning methods, then present a number of important deep learning approaches to solve super resolution problems, different architectures as well as up-sampling operations will be introduced. Afterwards, we focus on the applications of deep learning methods in medical imaging super resolution problems, the challenges to overcome will be presented as well