In a reverse microemulsion consisting of water, oil (octane), an anionic surfactant [aerosol OT (AOT)], and the reactants of the oscillating Belousov-Zhabotinsky (BZ) reaction, a variety of complex spatiotemporal patterns appear. These include traveling and standing waves, spirals that move either toward or away from their centers, spatiotemporal chaos, Turing patterns, segmented waves, and localized structures, both stationary and oscillatory. The system consists of nanometer-sized droplets of water containing the BZ reactants surrounded by a monolayer of AOT, swimming in a sea of oil, through which nonpolar BZ intermediates can diffuse rapidly. We present experimental and computational results on this fascinating system and comment on possible future directions for research. (C) 2005 American Institute of Physics.