A survey of recent theoretical and experimental studies on localized structures that form and propagate in a broad class of optical and matter-wave media is presented. The article is structured as a resource paper that overviews a large series of theoretical and experimental results obtained in diverse research areas: linear and nonlinear optical waveforms, nonlinear surface waves, ultrashort few-cycle optical pulses, localized structures in fractional systems, rogue (freak) waves, and matter-wave localized states. Key words: localized structures, optical media, Bose-Einstein condensates, solitons and vortices in fractional media, nonlinear surface waves, rogue waves, matter waves. The paper discusses recent advances in the study of localized structures in optical and matter-wave media. It covers topics such as spatiotemporal optical solitons, dissipative solitons, nonlinear surface waves, ultrashort optical pulses, and localized structures in fractional media. The paper also discusses the dynamics and stability of solitons in various physical contexts, including Bose-Einstein condensates and nonlinear optical media. It highlights recent theoretical and experimental results on the formation and propagation of localized structures, including dark and bright solitons, vortex solitons, and rogue waves. The paper also discusses the role of nonlinearities, such as Kerr-type nonlinearities, in the formation and stability of these structures. The paper concludes with a summary of the most relevant recent experimental and theoretical results for solitons in two-dimensional and three-dimensional optical media and Bose-Einstein condensates.A survey of recent theoretical and experimental studies on localized structures that form and propagate in a broad class of optical and matter-wave media is presented. The article is structured as a resource paper that overviews a large series of theoretical and experimental results obtained in diverse research areas: linear and nonlinear optical waveforms, nonlinear surface waves, ultrashort few-cycle optical pulses, localized structures in fractional systems, rogue (freak) waves, and matter-wave localized states. Key words: localized structures, optical media, Bose-Einstein condensates, solitons and vortices in fractional media, nonlinear surface waves, rogue waves, matter waves. The paper discusses recent advances in the study of localized structures in optical and matter-wave media. It covers topics such as spatiotemporal optical solitons, dissipative solitons, nonlinear surface waves, ultrashort optical pulses, and localized structures in fractional media. The paper also discusses the dynamics and stability of solitons in various physical contexts, including Bose-Einstein condensates and nonlinear optical media. It highlights recent theoretical and experimental results on the formation and propagation of localized structures, including dark and bright solitons, vortex solitons, and rogue waves. The paper also discusses the role of nonlinearities, such as Kerr-type nonlinearities, in the formation and stability of these structures. The paper concludes with a summary of the most relevant recent experimental and theoretical results for solitons in two-dimensional and three-dimensional optical media and Bose-Einstein condensates.