Accelerating MRI has been widely used in clinical medicine by reconstruction after undersampling in $k$-space and parallel MRI technology can effectively reduce the scanning time in MRI examination. Driven by deep learning technology which involved in accelerating MRI has made a breakthrough. Accelerating MRI based on deep learning has become the research hotspot in the field of MRI with its faster scanning and imaging. The high quality of MRI images with less artifacts can be reconstructed even with lower sample ratio. In this paper, we first briefly reviews the traditional accelerating MRI sampling methods and then introduce the joint optimization framework of under-sampling and reconstruction based on deep learning in accelerating MRI by comparing the performance of relevant frameworks. Finally, we discuss the development trend of accelerating MRI sampling.