Global competence has become a popular concept for engineering institutions around the world. Despite its recent emergence and still vague characteristics, it has been widely adopted by institutions aiming to prepare globally minded graduates. However, the concept's elusive and complex nature requires careful consideration in order to lead to impactful learning. This study provides a comprehensive overview of engineering institutions' practical efforts to foster global competence learning. Guided by a systematic literature review covering the last two decades, it provides a comprehensive account of work related to the concept. The study first explores institutions' practical efforts to promote global competence development, highlighting the most popular institutional approaches, including intercultural collaborations, mobility experiences, internationalization at home activities, and virtual collaborations. Furthermore, it critically analyzes how the concept is translated into practice, showing that practical efforts often lack guiding conceptualizations or reliable outcome assessments. To provide a thorough overview of institutional engagement with global competence, the study also highlights the geographical contexts of the universities involved in such efforts, as well as related chronological trends and developments, before concluding with reflections on the future of global competence education.