Stromatolites are laminated, lithified, sedimentary growth structures that accrete away from a point or limited surface of attachment. They are commonly, but not necessarily, of microbial origin and calcareous composition. Although familiar to geologists, they remain enigmatic as to origin and uncertain as to their full potential for historical geology.We summarize here the results of collective inquiry and discussion concerning central problems of stromatolite morphogenesis. We focus on relations between microstructure, laminar details, and gross morphology of ancient, probably biogenic, stromatolites and on the microbial composition and laminar characteristics of analogous modern microbial mats and sedimentary structures produced by them.The basic microstructure-determining unit of the modern stromatolite analog of biogenic origin is the mat-building community of organisms and particularly its dominant species, operating within a particular ecological setting. Biological factors dominate at the laminar and sublaminar level. Gross morphology probably reflects a balance between ecological processes and microbial activity.Nomenclatural clarity and stratigraphic utility turn on a proper understanding of morphogenesis. Although stromatolites will continue to function as stratigraphic and paleoecologic indicators, the reasons behind and limits to their applicability will remain obscure while morphogenetic processes remain uncertain. Finally, we outline some problems whose resolution could reduce that uncertainty.