When liquids or solid materials rotate, they impart centrifugal and/or shear forces. This Review surveys rotary devices and systems in which such forces control small-scale flows, self-organization phenomena, materials synthesis or chemical reactivity at molecular and macro-molecular levels. Centrifugal forces directed away from the rotation axis enable various separations or lab-on-a-disc systems and can shape interfaces or deposit thin films of functional materials. When these forces act on particles lighter than the rotating fluid, they can provide the basis for colloidal crystallization or trapping; when the direction of rotation changes, they can simulate microgravity conditions and affect motility patterns of living organisms. Shear forces, by contrast, can promote crystallization, couple to molecular-scale assembly and affect its chiral outcomes. Combining centrifugal and shear forces is useful in establishing rotating reactors to accelerate reaction kinetics, modulate chemical reactivity, enable multistep syntheses or support complex extractions. Through these and other examples, we illustrate that rotating reaction vessels can enable new types of chemical experimentation, with outcomes that are not always understood. We argue that rotating systems for studying such processes will become more common given advances in remotely controlled sensors and spectrometers that can monitor the contents of rotating vessels.