Technology education is a new school subject in comparison with other subjects within the Swedish compulsory school system. Research in technology education shows that technology teachers lack experience of and support for assessment in comparison with the long-term experiences that other teachers use in their subjects. This becomes especially apparent when technology teachers assess students' knowledge in and about technological systems. This study thematically analysed the assessment views of eleven technology teachers in a Swedish context. Through the use of in-depth semi-structured qualitative interviews, their elaborated thoughts on assessing knowledge about technological systems within the technology subject (for ages 13-16) were analysed. The aim was to describe the teachers' assessment views in terms of types of knowledge, and essential knowledge in relation to a progression from basic to advanced understanding of technological systems. The results showed three main themes that the interviewed teachers said they consider when performing their assessment of technological systems; understanding (a) a system's structure, (b) its relations outside the system boundary and (c) its historical context and technological change. Each theme included several underlying items that the teachers said they use in a progressive manner when they assess their students' basic, intermediate and advanced level of understanding technological systems. In conclusion, the results suggest that the analysed themes can provide a basis for further discussion about defining a progression for assessing students' understanding about technological systems. However, the findings also need to be examined critically as the interviewed teachers' views on required assessment levels showed an imbalance; few students were said to reach beyond the basic level, but at the same time most assessment items lay on the intermediate and advanced levels.