Low energy precision tests of fundamental symmetries provide excellent probes for the Beyond Standard Model Physics. Theoretical interpretations of these experiments often involve the application of non-perturbative Quantum Chromodynamics in the study of hadronic matrix elements that may either serve as signals of new physics or Standard Model backgrounds. In this work I present a series of studies on different hadronic matrix elements using various low-energy effective approaches to Quantum Chromodynamics, and discuss the impact of these studies on our knowledge of Standard Model and Beyond Standard Model physics.