In this talk I address recent advances regarding linear power corrections in collider processes, focusing on developments achieved within the large $\beta_0$ approximation framework. I present a general result that holds when massless partons are considered, offering a simplified approach to deriving both established and novel findings related to power corrections in collider processes. A key application of this result is the extension of linear power corrections calculations to hadronic shape variables in $e^+e^-$ annihilation, advancing from the two-jet to the three-jet regime. In this framework, I present recent fits to available LEP data and discuss the impact of the newly found corrections. Finally, I discuss recent results regarding massive partons, applied in particular to top production and decay processes.