Advances in nonequilibrium pattern formation in reaction-diffusion systems are reviewed. Special emphasis is placed on patterns found in the spatially extended Belousov-Zhabotinsky reaction dispersed in aerosol OT water-in-oil microemulsions (BZ-AOT system): Turing patterns, packet and standing waves, antispirals and segmented spirals, and accelerating waves and oscillons. All experimental results are explained theoretically and reproduced in computer simulations.