This empirically based chapter investigates how higher education students from a Colombian university explore the meaning and construction of third spaces in the development of their intercultural awareness and competence. Based on a narrative, critical-incident approach, a group of 14 undergraduates analyzed their real intercultural encounters. These narratives and subsequent semi-structured interviews led to important findings. For the most part, when confronted with critical incidents, students opted for proactive participation and engagement in third spaces. Some frequent strategies addressed unveiling conflict, establishing dialogue, valuing knowledge co-production, propitiating active listening, (re)accommodating power relations, and revisiting how one's cultural identity and that of others are (re)shaped in a transitory relationship that could lead to the strengthening of intercultural competence. Students advocate for critical incident analysis and how it can be applied as extended knowledge in future intercultural encounters and in their own intercultural growth.