We present an overview of the properties and applications of optical bistability in vertical-cavity semiconductor optical amplifiers (VCSOAs). The basic physics and analytical models of this optical nonlinearity are discussed. Experimental results obtained from a VCSOA operated in the 850 nm wavelength region are presented. Counterclockwise hysteresis loops are obtained over a range of initial phase detuning and bias currents. One hysteresis loop is observed experimentally with an input power as low as 2 muW when the device is biased at 98% of its lasing threshold. Numerical simulations based on the Fabry-Perot resonator model and rate equations we developed show good agreement with our experimental observations. In addition, a low input intensity high contrast (10:1) optical and gate and 2R regeneration are demonstrated. We believe that bistable VCSOAs can significantly advance the prospect of a dense two-dimensional array of low-switching-intensity all-optical logic and memory elements.