Stromatolites are attached, lithified sedimentary growth structures, accretionary away from a point or limited surface of initiation. Though the accretion process is commonly regarded to result from the sediment trapping or precipitation-inducing activities of microbial mats, little evidence of this process is preserved in most Precambrian stromatolites. The successful study and interpretation of stromatolites requires a process-based approach, oriented toward deconvolving the replacement textures of ancient stromatolites. The effects of diagenetic recrystallization first must be accounted for, followed by analysis of lamination textures and deduction of possible accretion mechanisms. Accretion hypotheses can be tested using numerical simulations based on modem stromatolite growth processes. Application of this approach has shown that stromatolites were originally formed largely through in situ precipitation of laminae during Archean and older Proterozoic times, but that younger Proterozoic stromatolites grew largely through the accretion of carbonate sediments, most likely through the physical process of microbial trapping and binding. This trend most likely reflects long-term evolution of the earth's environment rather than microbial communities.