This thesis is concerned with gauge theories, their complicated vacuum and resulting effects. After an introduction to the subject, it is divided into four parts.

Firstly, we treat the problem of chiral charge dynamics at finite temperature. Quantum field theory predicts a possibility for massless fermions to be transferred into electromagnetic fields with non-zero helicity and vice-versa. This phenomenon has applications ranging from cosmology to heavy-ions physics. We present a numerical investigation from first principles of the resulting complex dynamics and find a qualitative agreement with previous studies based on hydrodynamical approaches but measure rates that differ by up to an order of magnitude. We interpret this effect as contributions coming from small scales not previously taken into account.

Secondly, we present a study of open-boundary conditions in lattice QCD at finite temperature. They were designed to ease up the problem of "topological freezing", which plagues numerical simulations close to the continuum limit. In particular, we determine the length of the "boundary zone" for two different temperatures. We also use the boundary effects to extract screening masses.

Thirdly, we move on to present a compendium of lattice techniques, including some new algorithms, to perform real-time classical simulations of bosonic matter, Abelian and non-Abelian gauge fields in an expanding universe. We also briefly introduce CosmoLattice, a numerical software designed to perform such simulations, which are particularly interesting to study the reheating phase of our universe.

Finally, we study yet another technique to probe non-perturbative sectors of field theories. Namely, we show that one can reconstruct the Schwinger pair production rate, which is the rate of production of particles due to the presence of a strong electric field, using only a few terms of the weak magnetic field expansion. This surprising result is obtained by using techniques coming from the field of resurgence and the analysis of asymptotic expansions.

We conclude this work by presenting some general outlooks, sharing aspects of all these different yet related topics.