Student understanding of fundamental concepts in kinematics has been explored using the phenomenographic research method. University and high schoolphysics students were interviewed and their understandings of displacement, velocity, and frames of reference have been analyzed in particular problem contexts. Descriptions of the different ways students understand the concepts have been developed and relations between the different levels of understanding have been identified. The data highlight the contextual nature of learning and the need for teachers to focus on the nature of student understanding in specific contexts using questions that require qualitative explanation by students. In particular, it is demonstrated that success in mechanical, quantitative problem solving can mask inadequate understanding of basic concepts that hinders learning in later years of study of the subject. Implications for teaching and assessment are discussed.