Studying low-dimensional magnetic systems still attracts considerable attention of researchers. In fact, depending on the crystalline symmetry and distance between neighboring spin various magnetic configurations ranging from (anti)ferromagnet states to more complicated textures might emerge. If in addition, inversion symmetry is broken the spins alignment gains a certain chirality due to spin-orbit driven antisymmetric Dzyaloshinskii-Moriya interaction (DM). A certain class of nonlinear equations allow particle-like solution, solitary waves or solitons, which preserve their shape in the duration of their motion and collision processes. There also exists a class of topological solitons whose ground state can not be connected to their excited states and is characterized by some topological number. These particle-like states, e.g. magnetic soliton, skyrmion, domain wall, form a spatially localized clot of magnetic energy. Magnetic skyrmions are chiral spin structures with a whirling configurations so that the plane on which the spins are specified is topologically equivalent to a sphere. Because of that, a certain topological invariant, namely degree of mapping can be ascribed to the structure. The ground state configuration of magnetic structures can be understood by studying corresponding magnetization dynamics, which is based on the solution of phenomenologically derived Landau-Lifshitz equation expressing magnetization precession about effective field. This equation does not take account of dissipation which is physically meaningful and needs to be supplied with the Gilbert term responsible for relaxation. The spin waves are known to be quantized thus leading to the notion of magnons, that can be excited in magnetic materials. In most of spin-wave phenomena a number of magnons is a macroscopic quantity and can be well described by the Landau-Lifshitz equation. As a result, the concept of coherent magnon states analogous to that of quantum optics can be pushed forward. We discuss topologically protected magnetic solitons and skyrmions that might potentially be applied for logical operations and/or information storage in the rapidly advancing field of solitonics (and skyrmionics). The optical analogs will be also considered.