In the field of Software Engineering (SE), educational institutions are confronted with the demanding responsibility of aligning their curricula to provide students with the competencies — soft and technical — demanded by the evolving job market. Moreover, workplaces are becoming increasingly international, highlighting the competencies required in collaborating with people from diverse linguistic and cultural backgrounds. Competency models offer essential input for curriculum design. Moreover, educators may need to construct their own competency models when international guidelines fall short. To prepare students for future workplaces, curriculum designers necessitate knowledge to address demands of the international working environment. To gain a deeper understanding of the needs in the international SE context, we conducted a systematic literature review (SLR) to identify and analyze existing SE competency models and their construction, as well as investigate communication, collaboration, intercultural, and language competencies embedded in these models. This SLR identified 29 competency models across diverse application domains and purposes, constructed using a range of mono- and multi-method approaches, and offering multiple use scenarios for diverse stakeholders. We identified and collected an extensive collection of communication, collaboration, intercultural, and language competencies from the competency models in addition to the elements of the competency model construction process. Regarding identified competencies, communication and collaboration embody as core components in SE competency models whereas intercultural and language competencies are depreciated. Moreover, competency models and their construction lack international aspects. These findings highlight gaps in current competency models and offer insights into curriculum design to better prepare students for international SE environments.