The purpose of the study was to identify and categorise the criteria-specified instructional approaches to fostering undergraduates' cross-cultural skills involving training them in foreign languages and to evaluate their effectiveness and feasibility. It was a systemic review of the effectiveness type. The descriptive content analysis was used as a methodology within the study to analyse the relevant short-listed sources. The triangular assessment method (TAM) was applied by instructors from Ukraine to rate each approach's/programme/course's potential effectiveness and/or feasibility for the context of higher education in Ukraine. This review identified potentially effective and feasible approaches/programmes/courses that can be converged to produce more efficient instructional models for fostering undergraduates' cross-cultural skills. The selected approaches or courses or programmes could be categorised as technology-driven approaches, approaches based on classroom activities or using specific instruction models, psychological effect-driven approaches, and combined or converged approaches. The use of technology-driven approaches seems to be the emerging instructional trend specifically in training students' cross-cultural skills.