Oscillations pervade biological systems at all scales. In bacteria, oscillations control fundamental processes, including gene expression, cell cycle progression, cell division, DNA segregation and cell polarity. Oscillations are generated by biochemical oscillators that incorporate the periodic variation in a parameter over time to generate an oscillatory output. Temporal oscillators incorporate the periodic accumulation or activity of a protein to drive temporal cycles such as the cell and circadian cycles. Spatial oscillators incorporate the periodic variation in the localization of a protein to define subcellular positions such as the site of cell division and the localization of DNA. In this Review, we focus on the mechanisms of oscillators and discuss the design principles of temporal and spatial oscillatory systems.