Solvent-assisted block copolymer self-assembly is a compelling method for processing and advancing practical applications of these materials due to the exceptional level of the control of BCP morphology and significant acceleration of ordering kinetics. Despite substantial experimental and theoretical efforts devoted to understanding of solvent-assisted BCP film ordering, the development of a universal BCP patterning protocol remains elusive; possibly due to a multitude of factors which dictate the self-assembly scenario. The aim of this review is to aggregate both seminal reports and the latest progress in solvent-assisted directed self-assembly and to provide the reader with theoretical background, including the outline of BCP ordering thermodynamics and kinetics phenomena. We also indicate significant BCP research areas and emerging high-tech applications where solvent-assisted processing might play a dominant role.