The problems that are found in the real world, mathematics, and science are usually ill-defined problems. By contrast, the problems given in classrooms tend to be well-defined. It can be useful for students to solve modelling problems so they can learn how to deal with ill-defined problems. In a qualitative study of ninth to eleventh graders (N = 12) in different secondary school tracks in Germany, we investigated how students process modelling problems with missing data. We found that students have difficulties noticing when data are missing from some problems. When students notice the missing data, they notice it at the very beginning of their processing, after understanding the problem, or while validating the mathematical results. After noticing, either the students were able to make a realistic assumption about the missing data using various strategies, or they made no assumption at all. The theoretical and practical implications of the study are discussed.