In this talk, we present the analytic evaluation of the virtual corrections
to the di-muon production in electron-positron collision in QED, up to the second order in fine structure constant, retaining the full dependence on
the muon mass and considering the electron as a massless particle.
We discuss the computational details, and the high-level of automation it required,
from the diagram generation, to the amplitude decomposition, and to the evaluation of the master integrals,
along with the UV renormalization and the IR singularity structure.
We also present preliminary results on:
i) a crossing related process, such as the two-loop amplitude for muon-electron scattering in QED, relevant for the MUonE experiment;
ii) the extension to the process qqbar -> ttbar in QCD.