Recent years have witnessed increased interest in systems that are capable of supporting multistep chemical processes without the need for manual handling of intermediates. These systems have been based either on collections of batch reactors1 or on flow-chemistry designs2-4, both of which require considerable engineering effort to set up and control. Here we develop an out-of-equilibrium system in which different reaction zones self-organize into a geometry that can dictate the progress of an entire process sequence. Multiple (routinely around 10, and in some cases more than 20) immiscible or pairwise-immiscible liquids of different densities are placed into a rotating container, in which they experience a centrifugal force that dominates over surface tension. As a result, the liquids organize into concentric layers, with thicknesses as low as 150 micrometres and theoretically reaching tens of micrometres. The layers are robust, yet can be internally mixed by accelerating or decelerating the rotation, and each layer can be individually addressed, enabling the addition, sampling or even withdrawal of entire layers during rotation. These features are combined in proof-of-concept experiments that demonstrate, for example, multistep syntheses of small molecules of medicinal interest, simultaneous acid-base extractions, and selective separations from complex mixtures mediated by chemical shuttles. We propose that 'wall-less' concentric liquid reactors could become a useful addition to the toolbox of process chemistry at small to medium scales and, in a broader context, illustrate the advantages of transplanting material and/or chemical systems from traditional, static settings into a rotating frame of reference.