‘The Changing State of Gentrification’ (2001) by Jason Hackworth and the late Neil Smith is one of the most influential papers ever published in TESG. By introducing three waves, or periods, of practices and patterns of gentrification, it changed the way we think about gentrification. This Introduction to the Forum discusses the three waves introduced by Hackworth and Smith as well as fourth wave introduced by Lees et al. Finally, I will argue that during the global financial crisis we have entered fifth‐wave gentrification. Fifth‐wave gentrification is the urban materialisation of financialised or finance‐led capitalism. The state continues to play a leading role during the fifth wave, but is now supplemented – rather than displaced – by finance. It is characterised by the emergence of corporate landlords, highly leveraged housing, platform capitalism (e.g. Airbnb), transnational wealth elites using cities as a ‘safe deposit box’, and a further ‘naturalisation’ of state‐sponsored gentrification.