Carbonate concretions are common features of sedimentary rocks of all geological ages. They are most obvious in sandstones and mudstones as ovoid bodies of rock that protrude from natural outcrops: clearly harder or better cemented than their host rocks. Many people are excited by finding fossils in the centre of mudstone-hosted concretions (Fig. 1) but spend little time wondering why the fossils are so well preserved. While the study of concretions has benefitted from the use of advanced analytical equipment, simple observations in the field can also help to answer many questions. For example, in cliff sections, original sedimentary beds and sedimentary structures can be traced right through concretions (Fig. 2): so it can be deduced that the concretion clearly formed after these depositional structures were laid down. In this article we explain how and where concretions form and discuss the evidence, ranging from outcrop data to sophisticated laboratory analyses, which can be used to determine their origins. The roles of microbes, decaying carcasses, compaction and groundwaters are highlighted. Concretions not only preserve fossils but can also subdivide oil, gas and water reservoirs into separate compartments.