Pulsed terahertz (THz) electric fields enable various coherent THz imaging modes, such as reflection tomography, spectral imaging, and computed tomography (CT) for nondestructive inspection, quality control, and material characterization. The extension of coherent THz imaging modes to moving objects has been regarded as key to their social implementation. This Tutorial focuses on two-dimensional spatiotemporal (2D-ST) THz imaging of objects moving in one direction with constant speed as a promising means of enabling real-time coherent THz imaging. In 2D-ST THz imaging, the temporal waveform and line image of the THz pulse are simultaneously acquired without the need for mechanical scanning of the time delay and sample position using a combination of non-collinear 2D free-space electro-optic sampling with THz line-imaging optics. This 2D-ST THz imaging boosts the imaging rates of THz reflection tomography, THz spectral imaging, and THz CT to levels that are applicable to moving objects. The advanced THz reflection tomography and THz spectral imaging that result from the assistance of 2D-ST THz imaging achieve real-time line imaging of cross sections and spectral signatures, respectively. Subsequently, this enables in-line total inspection of objects moving on a translation stage or a conveyor belt. A THz CT system using real-time line projection of a THz beam is effectively applied to a 2D spectral cross section of a continuously rotating object. 2D-ST THz imaging enables the functional THz imaging of moving objects in various practical applications.