Domain walls are topological solitons that appear in many physical systems (phase transitions, condensed matter etc). They represent transition layers between two states corresponding to the wells of a certain potential function. We will start by presenting the domain walls in the Allen-Cahn model where the potential has a finite number of wells; in particular, we will study their symmetry and energy level. Next we study the case of Ginzburg-Landau type models where the potential has a continuum of wells. For well-posedness, the divergence-free constraint is imposed on the order parameter. In this case, we will study one-dimensional symmetry of domain walls as well as the nucleation of microstructures according to the shape of the potential function.