Runaway massive stars are the result of dynamical ejection during the formation process of young star-forming regions or the disruption of a close binary system when the more massive component explodes as a supernova. Runaway stars can be identified by their high peculiar velocities and/or their large z-heights above the Galactic plane. In the current paradigm for massive star evolution, classical Wolf-Rayet stars are the descendants of O stars with initial masses above 25 solar masses and have lifetimes less than 7 million years. In this talk, I describe how Gaia DR3 astrometric data is used to identify runaway Wolf-Rayet stars in the Galaxy. The trajectories of the runaways are then integrated backwards in time in order to infer kinematical ages and possible ejection mechanisms. I analyse the differences that are found in the spatial distributions and kinematical ages of runaways with different Wolf-Rayet subtypes. A few sources have inferred kinematic ages in excess of 7 million years, suggesting that binary evolution has played a significant role in their lives. I discuss the runaway frequency and characteristics in the context of stellar evolution models.