There is an increasing emphasis on assessing student learning outcomes from study abroad experiences, but this assessment often focuses on a limited range of outcomes and assessment methods. We argue for shifting to assessing student learning "processes" in study abroad and present the critical incident technique as one approach to achieve this goal. We demonstrate this approach in interviews with 79 students across a range of global engineering programs, through which we identified 173 incidents which were analyzed to identify common themes. This analysis revealed that students described a wide range of experiences and outcomes from their time abroad. Students' experiences were messy and complex, making them challenging to understand through typical assessment approaches. Our findings emphasize the importance of using a range of assessment approaches and suggest that exploring students' learning processes in addition to learning outcomes could provide new insights to inform the design of study abroad programs.