High-energy hadrons are absorbed in dense matter through a process called shower development. In this process, large numbers of soft neutrons are produced. These neutrons, which carry in total typically ∼10% of the shower energy, deposit this energy in ways very different from that for the charged shower components. This has important consequences for calorimetry, the particle detection technique based on total absorption of the objects to be measured. These consequences range from very beneficial (e.g., compensation) to very detrimental (e.g., the "Texas Tower effect"). In this article, the role played by neutrons in the formation of calorimeter signals is reviewed. The consequences for calorimetry in practical experiments are investigated.