Higgs and Beyond the Standard Model: from LHC to future colliders

<!--HTML--><p>BSM is turning 50 this year: the SM was not yet established experimentally that attempts to overcome its limitations and to offer an even more unified view of the laws of Nature started. Today, outstanding problems in particle physics and cosmology still call for BSM physics. And its quest remains an active field of research that requires intense collaborations between experimentalists and theorists. In this talk, I shall review what has been learnt from the LHC, in particular thanks to the observation of the Higgs boson and the first measurements of its properties, and what could still be revealed in particular at future colliders.</p>