This work demonstrates that the principles underlying phase-contrast MRI may be used to encode spatial rather than flow information along a perpendicular dimension, if this dimension contains an MRI-visible object at only one spatial location. In particular, the situation applies to 3D mapping of curved 2D structures which requires only two projection images with different spatial phase-encoding gradients. These phase-contrast gradients define the field of view and mean spin-density positions of the object in the perpendicular dimension by respective phase differences. When combined with highly undersampled radial fast low angle shot (FLASH) and image reconstruction by regularized nonlinear inversion, spatial phase-contrast MRI allows for dynamic 3D mapping of 2D structures in real time. First examples include 3D MRI movies of the acting human hand at a temporal resolution of 50 ms. With an even simpler technique, 3D maps of curved 1D structures may be obtained from only three acquisitions of a frequency-encoded MRI signal with two perpendicular phase encodings. Here, 3D MRI movies of a rapidly rotating banana were obtained at 5 ms resolution or 200 frames per second. In conclusion, spatial phase-contrast 3D MRI of 2D or 1D structures is respective two or four orders of magnitude faster than conventional 3D MRI. Magn Reson Med, 2011. © 2011 Wiley-Liss, Inc.