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Domain walls, two-dimensional topological defects that may emerge in spontaneous symmetry breaking phase transitions in the early universe, serve as a bridge between cosmology and particle physics and might therefore provide a unique window to probe theoriesbeyond the Standard Model of Particle Physics. In a cosmological setting, domain wallswould form extended networks, which typically approach a scaling regime with roughly asingle wall per Hubble patch. Stable domain walls that were to survive until the presentday, however, are heavily constrained by astrophysical observations to be very light.Walls, on the other hand, could also decay earlier in the evolution of the universe throughvarious mechanisms, in which case they could evade these strict limits on their massscale. This is the case, for instance, for biased domain walls that are predicted in manyrelevant beyond standard model scenarios. These may then have played a more relevant cosmological role and might therefore be easier for us to detect. A crucial elementin understanding possible observational signatures of domain wall networks is a precisecharacterization of their dynamics. This thesis explores the theoretical, numerical, and observational aspects of domain wall evolution, with a particular focus on their gravitationalwave signatures.
We begin with an overview of the cosmological standard model and the role of scalarfields in early universe physics, emphasizing their connection to topological defects. Weexplore the formation of such defects and discuss the state-of-the-art understanding ofdomain wall physics. In this context, we review the Velocity-dependent One-Scale model,which has evolved to be the standard analytical model in describing large-scale dynamicsof domain wall networks, as well as the more recent Parameter-Free Model.