We present an overview of the capabilities that the International Linear Collider (ILC) offers for precision measurements that probe the Standard Model. First, we discuss the improvements that the ILC will make in precision electroweak observables, both from W boson production and radiative return to the Z at 250 GeV in the center of mass and from a dedicated GigaZ stage of running at the Z pole. We then present new results on precision measurements of fermion pair production, including the production of b and t quarks. We update the ILC projections for the determination of Higgs boson couplings through a Standard Model Effective Field Theory fit taking into account the new information on precision electroweak constraints. Finally, we review the capabilities of the ILC to measure the Higgs boson self-coupling.