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We review 2-D spatiotemporal (2D-ST) terahertz (THz) imaging based on noncollinear free-space electrooptic sampling and its application to THz reflection tomography, THz spectral imaging, and THz spectral computed tomography (CT). 2D-ST THz imaging enables high-speed image acquisition at much higher rates than previously. Two-dimensional THz reflection tomography was effective for visualizing the internal structure of a moving paint film. A THz color scanner demonstrated the potential of rapid nondestructive inspection of moving pharmaceutical tablets. A THz spectral CT system using real-time line projection of a THz beam was effectively applied to a continuously rotating object. 2D-ST THz imaging enables functional THz imaging of moving objects in various practical applications.