The theoretical lower limit of subthreshold swing in MOSFETs (60 mV/decade) significantly restricts low voltage operation since it results in a low ON to OFF current ratio at low supply voltages. This paper investigates extremely-low power circuits based on new Si/SiGe HEterojunction Tunneling Transistors (HETTs) that have subthreshold swing < 60 mV/decade. Device characteristics as determined through Technology Computer Aided Design (TCAD) tools are used to develop a Verilog-A device model to simulate and evaluate a range of HETT-based circuits. We show that a HETT-based ring oscillator (RO) shows a 9-19X reduction in dynamic power compared to a CMOS RO. We also explore two key differences between HETTs and traditional MOSFETs, namely asymmetric current flow and increased Miller capacitance, analyzing their effect on circuit behavior and proposing methods to address them. Finally, HETT characteristics have the most dramatic impact on SRAM operation and hence we propose a novel 7-transistor HETT-based SRAM cell topology to overcome, and take advantage of, the asymmetric current flow. This new HETT SRAM design achieves 7-37X reduction in leakage power compared to CMOS.