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Mathematics is of utmost importance in engineering courses but studies on engineering students' conceptions of understanding in mathematics learning are found lacking in the literature. Therefore, this research attempts to address the above issue by answering the research question: "What are engineering students' conceptions of understanding in mathematics learning?" It employs the grounded theory methodology (Strauss & Corbin, 1990, 1998) and data are collected from in depth interviews with a total of 21 students and six lecturers. The substantive theory of engineering mathematics understanding (comprising of conceptual, functional, procedural, disciplinary and associational understanding) emerges in this study. The emergence of functional, disciplinary and associational understanding is unique in the context of engineering mathematics learning and has implications on successful engineering problem solving. (Contains 5 figures and 2 tables.)