Picosecond switching speeds and folded current-voltage characteristics have made quantum tunneling devices promising alternatives for high-speed and compact VLSI circuit design. This paper describes new bistable digital logic circuit topologies that use resonant tunneling diodes (RTDs) in conjunction with hetero-junction bipolar transistors (HBTs) and modulation-doped field effect transistors (MODFETs). The designed circuits include a single-gate, self-latching MAJORITY function besides basic NAND, NOR and inverter gates. The application of these circuits in the design of high-performance adders and parallel correlators is discussed. We also review multiple-valued logic (MVL) applications of RTDs that achieve significant compaction in terms of device count over comparable binary logic implementations in conventional technologies. These include a four-valued 4:1 multiplexer using 13 resonant tunneling bipolar transistors (RTBTs) and HBTs, a mask programmable four-valued, single-input gate using 4 RTDs and 14 HBTs, and a four-step countdown circuit using 1 RTD and 3 HBTs.