This article takes the subject of visual arts in Sweden as the point of departure in a discussion of how, with the help of portfolios, assessments may extend to include both the unpredictable and the ambiguous. The notion that assessments of learning outcomes must be either limited to superficial knowledge or completely arbitrary is shown to be a misconception. The author has made a study of the progression of young people's creativity in the visual arts from preschool to upper secondary school. The assessment was based on both product criteria and process criteria (investigative work, inventiveness, ability to use models, capacity for self-assessment). The materials assessed were portfolios of work containing sketches, drafts and finished works, log books, sources of inspiration and videotaped interviews with the students. Is there any progression in students' visual design, in their ability to work independently and assess their work? What is the degree of correlation in the assessments of different judges of student portfolios? These are some of the questions that this article attempts to answer, which concludes with a discussion of how schools can build a culture of learning that fosters the creative powers of young people.