We propose low-rank MR-MOTUS, a framework for real-time reconstructions of 3D respiratory motion-fields for MR-guided radiotherapy. Low-rank MR-MOTUS factorizes space-time motion-fields into static spatial components and dynamic temporal components. This allows to 1) exploit spatial and temporal correlations in motion, and 2) split the reconstruction into a large-scale off-line training phase, and a small-scale on-line inference phase. Results show that in the on-line inference phase 3D respiratory motion can be estimated in 130ms, from data acquired in 24ms. This yields a total latency of 154ms, and low-rank MR-MOTUS thereby paves the way for real-time MR-guided radiotherapy on the MR-linac.