Through precision straits to next standard model heights

After the LHC Run 1, the standard model (SM) of particle physics has been completed. Yet, despite its successes, the SM has shortcomings vis-à-vis cosmological and other observations. At the same time, while the LHC restarts for Run 2 at 13 TeV, there is presently a lack of direct evidence for new physics phenomena at the accelerator energy frontier. From this state of affairs arises the need for a consistent theoretical framework in which deviations from the SM predictions can be calculated and compared to precision measurements. Such a framework should be able to comprehensively make use of all measurements in all sectors of particle physics, including LHC Higgs measurements, past electroweak precision data, electric dipole moment, $g-2,$ penguins and flavor physics, neutrino scattering, deep inelastic scattering, low-energy $e^{+}{e}^{-}$ scattering, mass measurements, and any search for physics beyond the SM. By simultaneously describing all existing measurements, this framework then becomes an intermediate step, pointing us toward the next SM, and hopefully revealing the underlying symmetries. We review the role that the standard model effective field theory (SMEFT) could play in this context, as a consistent, complete, and calculable generalization of the SM in the absence of light new physics. We discuss the relationship of the SMEFT with the existing kappa-framework for Higgs boson couplings characterization and the use of pseudo-observables, that insulate experimental results from refinements due to ever-improving calculations. The LHC context, as well as that of previous and future accelerators and experiments, is also addressed.