Chemical gardens are perhaps the best example in chemistry of a self-organizing nonequilibrium process that creates complex structures. Many different chemical systems and materials can form these self-assembling structures, which span at least eight orders of magnitude in size, from nanometers to meters. Key to this magic is the self-propagation under fluid advection of reaction zones forming semipermeable precipitation membranes that maintain steep concentration gradients, with osmosis and buoyancy as the driving forces for fluid flow. Chemical gardens have been studied from the alchemists onwards, but now in the 2|st century we are beginning to understand how they can lead us to a new domain of self-organized structures of semipermeable membranes and (amorphous as well as polycrystalline) solids produced at the interface of chemistry, fluid dynamics, and materials science. We call this emerging field chemobrionics.