Wish-list for Run II top quark measurements (for BSM)

In this contribution I will highlight the new challenges for top quark physics at LHC Run II, focusing in particular on the interplay between precision studies on the top quark and searches for new physics. A new strategy to search for subtle scenarios of new physics is envisaged. The ability of compute and measure very accurately top quark properties such as its production rate, decay properties, e.g rates and distributions, and variables sensitive to the top quark mass is put at the center of this strategy to probe new physics.