The Standard Model (SM) has been tremendously successful in explaining all
particle physics observations so far. However, there are strong indications that yet
unknown particles and/or interactions have to exist. The Precision, or Low-Energy
frontier of the Standard Model aims at detecting effects of this New Physics as
deviations from the SM predictions in low-energy observables, and the precision of
measurements and calculations of these observables is in direct correspondence with
the scale at which the New Physics emerges. This requires understanding the SM at
low energies, most notably the Quantum Chromodynamics (QCD), the theory of strong
interactions. QCD explains the strongly interacting matter and its properties in
terms of quarks and gluons, and it is a complicated multi-scale problem. The
detailed understanding of the QCD in the non-perturbative regime is lacking, and a
joined effort from Lattice, Effective Field Theories and Phenomenology is necessary.
On the example of the parity-violating electron scattering and light muonic atoms I
will review how state-of-the-art calculations helped improving the precision of the
SM predictions in the kinematics of running and upcoming experiments, and motivated
new dedicated experiments.