Distinguishing from the widely used focal-plane-array imaging (e.g., the charge coupled device, CCD), another novel imaging scheme, computational ghost imaging (which is also called single-pixel imaging or correlated imaging) acquires object’s image by computing the correlations between the varied illuminating field and the imaging target with a no-spatial-resolution detector (single-pixel detector). Comparing with the well-developed silicon-based focal-plane-array cameras, computational ghost imaging is simpler, smaller, and, most significantly, can operate efficiently across a much broader spectral range. Moreover, this imaging methodology can be combined with some novel acquisition technologies, such as compressed sensing and adaptive imaging, making it suitable for many specific imaging applications. On the other hand, terahertz (THz) waves, covering the frequencies ranging from 0.1 THz to 10 THz, have many unique properties, such as the spectral fingerprint, high transmittance in most polar materials, high absorption by water, non-ionizing photon energy (1 THz, 4 meV). There are a lot of applications within THz waves, covering the fields of medical and biology sciences, non-destructive detection, security check, high-speed wireless communication and so on. Imaging with THz waves is also significant in many situations. However, since the focal-plane-array detector available within THz waves is expensive or complicated to fabricate, the main method for THz wave imaging was usually based on raster scanning. The computational ghost imaging within THz waves was firstly demonstrated in 2008, which paves a new route for THz wave imaging and inspires many applications including sub-diffraction-limit THz wave imaging and spatially resolved photoconductivity of graphene. In this article, we firstly review the historical developing process of ghost imaging, namely from the quantum ghost imaging to classical ghost imaging and then to computational ghost imaging. Secondly, the computational ghost imaging is described mathematically in details, including the linear mapping during the imaging process, algorithm for recovering the ghost image and a discussion about the performance of various measurement matrices in noisy imaging environment. And then, we introduce several computational ghost imaging applications within THz waves, including the first demonstration of THz wave computational ghost imaging, the invention of the dynamic spatial THz wave modulator, the sub-diffraction-limit THz wave computational ghost imaging and the photoconductivity mapping of graphene in THz region. At last, we outlook the prospects of the THz wave computational ghost imaging. We hope this review article can help the readers better understand the principles, applications, and prospects of the THz wave computational ghost imaging.