Zero-order ultrasensitivity was first described by Albert Goldbeter and Daniel Koshland, Jr in 1981 in a paper in the Proceedings of the National Academy of Sciences.  They showed using mathematical modeling that modification of enzymes operating outside of first order kinetics required only small changes in the concentration of the effector to produce larger changes in the amount of modified protein. This amplification provided added sensitivity in biological control, and implicated the importance of this in many biological systems.
Many biological processes are binary (ON-OFF), such as cell fate decisions, metabolic states, and signaling pathways. Ultrasensitivity is a switch that helps decision-making in such biological processes. For example, in apoptotic process, a model showed that a positive feedback of inhibition of caspase 3 (Casp3) and Casp9 by inhibitors of apoptosis can bring about ultrasensitivity (bistability). This positive feedback cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation (switch ON), which leads to cell apoptosis. Another model also showed similar but different positive feedback controls in Bcl-2 family proteins in apoptotic process.
Recently, Jeyeraman et al. have proposed that the phenomenon of ultrasensitivity may be further subdivided into three sub-regimes, separated by sharp stimulus threshold values: OFF, OFF-ON-OFF, and ON. Based on their model, they proposed that this sub-regime of ultrasensitivity, OFF-ON-OFF, is like a switch-like adaption which can be  accomplished by coupling N phosphorylation–dephosphorylation cycles unidirectionally, without any explicit feedback loops.
Other recent work has emphasized that not only is the topology of networks important for creating ultrasensitivity responses, but that their composition (enzymes vs. transcription factors) strongly affects whether they will exhibit robust ultrasensitivity.  Mathematical modeling suggests for a broad array of network topologies that a combination of enzymes and transcription factors tends to provide more robust ultrasensitivity than that seen in networks composed entirely of transcription factors or composed entirely of enzymes.