For three billion years, before the Cambrian diversification of life, laminated carbonate build-ups called stromatolites were widespread in shallow marine seas. These ancient structures are generally thought to be microbial in origin and potentially preserve evidence of the Earth's earliest biosphere. Despite their evolutionary significance, little is known about stromatolite formation, especially the relative roles of microbial and environmental factors in stromatolite accretion. Here we show that growth of modern marine stromatolites represents a dynamic balance between sedimentation and intermittent lithification of cyanobacterial mats. Periods of rapid sediment accretion, during which stromatolite surfaces are dominated by pioneer communities of gliding filamentous cyanobacteria, alternate with hiatal intervals. These discontinuities in sedimentation are characterized by development of surface films of exopolymer and subsequent heterotrophic bacterial decomposition, forming thin crusts of microcrystalline carbonate. During prolonged hiatal periods, climax communities develop, which include endolithic coccoid cyanobacteria. These coccoids modify the sediment, forming thicker lithified laminae. Preservation of lithified layers at depth creates millimetre-scale lamination. This simple model of modern marine stromatolite growth may be applicable to ancient stromatolites.