Owing to the unprecedented development in terahertz (THz) sources and detectors in the last decade, technologists and researchers have intensified their efforts to develop advanced THz sensing and imaging systems with superior performance and unique functionalities. One of the key elements to realize such systems is the ability to monolithically integrate high-performance semiconductor devices with THz antennas and other passive structures. In recent years, devices based on interband tunneling in III-V heterostructures have emerged as promising candidates for THz detection that offer extremely high nonlinearity, high sensitivity, low noise, fast response, and room temperature operation. In this paper, we first review the development of heterostructure backward tunnel diodes (HBDs) in the InAs/AlSb/AlGaSb material system that have been demonstrated with detection sensitivity that outperforms the current state of the art (e.g., the fundamental limit of Schottky diodes) and with noise-equivalent power (NEP) below 0.2 pW/Hz½. We then present the monolithic integration of HBDs with planar folded dipole antennas (FDAs) using submicrometer-scale airbridges to achieve optimized impedance matching for high-performance and compact THz detectors and focal-plane array (FPA) imaging systems. In addition, the potential of using HBDs for realizing THz systems with advanced functionalities such as spectroscopic FPAs (using frequency-tunable THz antennas) and polariametric detection/imaging systems will be discussed. Finally, the integration of HBDs into waveguides for more advanced THz sensing and imaging (e.g., a six-port reflectometer for near-field imaging) will be discussed.