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This paper reviews recent advances in the design and performance of our original InP- and GaAs-based plasmonic high-electron-mobility transistors (HEMTs) for ultrahighly-sensitive terahertz (THz) sensing and imaging. First, the fundamental theory of plasmonic THz detection is briefly described. Second, single-gate HEMTs with parasitic antennae are introduced as a basic core device structure, and their detection characteristics and sub-THz imaging potentialities are investigated. Third, dual-grating-gate (DGG)-HEMT structures are investigated for broadband highly sensitive detection of THz radiations, and the record sensitivity and the highly-sensitive THz imaging are demonstrated using the InP-based asymmetric DGG-HEMTs. Finally, the obtained results are summarized and future trends are addressed.