Accurate predictions in perturbative QCD require the calculation of physical observables beyond leading order accuracy. However, the evaluation of higher order radiative corrections to fully differential cross sections is hampered by the presence of infrared singularities in intermediate stages of the calculation. A possible way to consistently treat infrared singularities is through a subtraction algorithm. In this talk, I will describe the CoLoRFulNNLO method, a completely local subtraction scheme for fully differential predictions at NNLO in QCD. I will give an overview of the main conceptual issues that need to be addressed as well as touch on some technical aspects. I will also discuss the implementation of the CoLoRFulNNLO framework in the parton level Monte Carlo code MCCSM. As a first application, I will revisit the computation of event shape observables in electron-positron annihilation and present new predictions for some event shapes at NNLO accuracy.
