In this White Paper for the 2021 Snowmass process, we detail the status and prospects for dual-readout calorimetry. While all calorimeters allow estimation of energy depositions in their active material, dual-readout calorimeters aim to provide additional information on the light produced in the sensitive media via, for example, wavelength and polarization, and/or a precision timing measurements, allowing an estimation of the shower-by-shower particle content. Utilizing this knowledge of the shower particle content may allow unprecedented energy resolution for hadronic particles and jets, and new types of particle flow algorithms. We also discuss the impact continued development of this kind of calorimetry could have on precision on Higgs boson property measurements at future colliders.