BabaYaga@NLO at present and future $e^+e^-$ colliders. Celebrating 25 years of BabaYaga

Precise QED radiative corrections for low- and high-energy electron-positron colliders are essential for accurate simulations of luminosity processes and precision tests of the Standard Model. We review the historical formulation and the recent developments of the BabaYaga@NLO event generator, which implements a QED Parton Shower matched with fixed-order calculations. We discuss the theoretical formulation of the code, as well as the assessment of its theoretical accuracy. Applications at low- and high-energy $e^+e^-$ colliders are presented, including latest result, together with the perspectives for future improvements, in view of the demanding precision requirements of future machines at the intensity frontier.