In this White Paper for the 2021 Snowmass process, we discuss aspects of precision timing within electromagnetic and hadronic calorimeter systems for highenergy physics collider experiments. Areas of applications include particle identification, event and object reconstruction, and pileup mitigation. Two different system options are considered, namely cell-level timing capabilities covering the full detector volume, and dedicated timing layers integrated in calorimeter systems. A selection of technologies for the different approaches is also discussed.