Traditional terahertz (THz) equipment faces major obstacles in providing the system cost and compactness necessary for widespread deployment of THz applications. Because of this, the field of THz integrated circuit (THz IC) design in CMOS and SiGe HBT technologies has surged in the last decade. An interplay of advances in silicon process technology, design technique, and microelectronic packaging promises to narrow the gap between the requirements and the reality of system cost and performance of THz components. Furthermore, the scalability, reconfigurability, and signal processing features of silicon technology have initiated research in complex THz ICs that expand the functionality of THz systems; this has enabled new applications, methods, and algorithms. This paper reviews the progress in THz IC research and investigates several realizations of THz imaging and sensing applications with silicon-based components regarding their motivation, system performance, and challenges. THz computed tomography, broadband multicolor imaging, high-resolution FMCW radar imaging, subwavelength resolution near-field imaging, and compressed sensing are presented.