This chapter argues that control of magnetic domains and domain wall structures is one of the most important issues from the viewpoint of both applied and basic research in magnetism. Its discussion is however limited to static and dynamic properties of magnetic vortex structures. It has been revealed both theoretically and experimentally that for particular ranges of dimensions of cylindrical and other magnetic elements, a curling in-plane spin configuration is energetically favored, with a small region of the out-of-plane magnetization appearing at the core of the vortex. Such a system, which is sometimes referred to as a magnetic soliton, is characterized by two binary properties: A chirality and a polarity, each of which suggests an independent bit of information in future high-density nonvolatile recording media.