In the first part, Gino Isidori will review the theoretical interest of Bs -> mu mu, both within and beyond the SM, discussing in particular the uncertainties affecting the SM prediction. Then Xabier Cid Vidal will explain the search for Bs -> mu mu using 2.1 fb^-1 of LHCb data, leading to a 3.5sigma evidence. He will describe the experimental challenges of this channel and summarize the techniques employed.