The reconstruction of the signal from hadrons and jets emerging from the proton–proton collisions at the Large Hadron Collider (LHC) and entering the ATLAS calorimeters is based on a three-dimensional topological clustering of individual calorimeter cell signals. The cluster formation follows cell signal-significance patterns generated by electromagnetic and hadronic showers. In this, the clustering algorithm implicitly performs a topological noise suppression by removing cells with insignificant signals which are not in close proximity to cells with significant signals. The resulting topological cell clusters have shape and location information, which is exploited to apply a local energy calibration and corrections depending on the nature of the cluster. Topological cell clustering is established as a well-performing calorimeter signal definition for jet and missing transverse momentum reconstruction in ATLAS.