  Motion represents one of the major challenges in magnetic resonance imaging
(MRI). Since the MR signal is acquired in frequency space, any motion of the
imaged object leads to complex artefacts in the reconstructed image in addition
to other MR imaging artefacts. Deep learning has been frequently proposed for
motion correction at several stages of the reconstruction process. The wide
range of MR acquisition sequences, anatomies and pathologies of interest, and
motion patterns (rigid vs. deformable and random vs. regular) makes a
comprehensive solution unlikely. To facilitate the transfer of ideas between
different applications, this review provides a detailed overview of proposed
methods for learning-based motion correction in MRI together with their common
challenges and potentials. This review identifies differences and synergies in
underlying data usage, architectures, training and evaluation strategies. We
critically discuss general trends and outline future directions, with the aim
to enhance interaction between different application areas and research fields.
