At a time when the particle physics community is trying to decide what the next large particle collider experiment may be, it becomes crucial to study and establish the potential for indirect tests of new physics at the different projects that have been proposed, in order to make an informed decision. In the absence of a clear indication of what the new physics beyond the Standard Model may be, a model-independent approach for such studies is preferred, to make sure we cover all possibilities. In this talk, I will discuss some of the studies that were prepared for the 2020 Update of the European Strategy for Particle Physics and later updated during the 2021 Snowmass process using the general formalism of the Standard Model Effective Field Theory, with emphasis on the physics of the electroweak and Higgs sectors.