This paper presents an overview of several methods for modeling domain walls in weak ferromagnets, with a focus on their relevance to the development of memory and logic devices. Utilizing the Landau-Lifshitz theoretical framework, we analyze the distributions of total magnetic energy and magnetization in ferromagnetic crystals with an easy axis of magnetization. The study examines the structure and dynamics of both Bloch and Néel domain walls, highlighting the influence of exchange and anisotropy energies on wall width and profile. Special attention is given to the behavior of domain walls at the nanoscale, where their properties can be significantly altered by geometry and external stimuli such as electric currents. The dynamics of domain wall motion are described using the Landau-Lifshitz-Gilbert equation, and soliton solutions to the sine-Gordon equation are discussed as models for 180-degree domain boundaries. The results emphasize the potential for controlled domain wall manipulation in nanostructures, which is essential for high-density, energy-efficient magnetic memory and logic applications.