During magnetic resonance imaging, motion and flow artifacts often severely decrease image quality. The mechanisms of these kinds of artifacts are very complex. This article reviewed the pre-handling techniques of motion and flow artifacts, such as changing magnetic resonance imaging parameters, using spatial pre-saturation pulse sequences, gating and triggering techniques of suppressing respiratory motion artifact, as well as the progress of magnetic resonance pulse sequences in suppressing motion and flow artifacts, The paper briefly introduced post-processing techniques of suppressing motion and flow artifacts.