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Reducing supply voltage is a promising way to address the power dissipation in nano-electronic circuits. However, the fundamental lower limit of subthreshold slope (SS) within metal oxide semiconductor field effect transistors (MOSFETs) is a major obstacle to further scaling the operation voltage without degrading ON/OFF ratio in current integrated circuits. Tunnel field-effect transistors (TFETs) benefit from steep switching characteristics due to the quantum-mechanical tunneling injection of carriers from source to channel, rather than by conventional thermionic emission in MOSFETs. TFETs based on group III-V compound semiconductor materials further improve the ON-state current and reduce SS due to the low band gap energies and smaller carrier tunneling mass. The mixed arsenide/antimonide (As/Sb) InxGa1-xAs/GaAsySb1-y heterostructures allow a wide range of band gap energies and various staggered band alignments depending on the alloy compositions in the source and channel materials. Band alignments at source/channel heterointerface can be well modulated by carefully controlling the compositions of the mixed As/Sb material system. In particular, this review introduces and summarizes the progress in the development and optimization of low-power TFETs using mixed As/Sb based heterostructures including basic working principles, design considerations, material growth, interface engineering, material characterization, device fabrication, device performance investigation, band alignment determination, and high temperature reliability. A review of TFETs using mixed As/Sb based heterostructures shows superior structural properties and distinguished device performance, both of which indicate the mixed As/Sb staggered gap TFET as a promising option for high-performance, low-standby power, and energy-efficient logic circuit application.