In this study we provide a systematic characterization of Rossby wave activity during the 25 sudden stratospheric warming (SSW) and 31 strong polar vortex (SPV) events that occurred in the period 1979–2021, identifying the specific tropospheric and stratospheric waves displaying anomalous behaviour during such events. Space–time spectral analysis is applied to ERA5 data for this purpose, so that both the wavenumber and the zonal phase speed of the waves can be assessed. We find that SSW events are associated with a reduction in the phase speed of Rossby waves, first in the stratosphere and then in the troposphere; SPV events are tied to a simultaneous increase of phase speed across vertical levels. Phase speed anomalies become significant around the event and persist for 2–3 weeks afterwards. Changes of Rossby wave properties in the stratosphere during SSW and SPV events are dominated by changes in the background flow, with a systematic reduction or increase, respectively, in eastward propagation of the waves across most wavenumbers. In the troposphere, on the other hand, the effect of the background flow is also complemented by changes in wave properties, with a shift towards higher wavenumbers during SSW events and towards lower wavenumbers for SPV events. The opposite response between SSW and SPV events is also visible in the meridional heat and momentum flux co-spectra, which highlight from a novel perspective the connection between stratospheric Rossby waves and upward propagation of waves.