Searching for new physics with precision measurements at LHC and future colliders

The search for New Physics at colliders can take many shapes, and while
direct searches for new particles are definitely a necessity, a strong
program of precision measurements together with precision calculations of
the Standard Model predictions could bring us information on beyond Standard
Model physics even without new resonances at collider.  In this talk I will
review some of the advantages and drawbacks of this approach, with an eye to
the capabilities of future accelerators, and with special focus on the use
of Effective Field Theories that have proved to be an invaluable tool for
understanding and interpreting the results of indirect searches.