We report on a focused workshop of The Leukemia and Lymphoma Society that was held at Goldsmiths, University of London in 2008. During this workshop we discussed new clinical and experimental data in chronic myeloid leukemia (CML) research, particularly focusing on the validity (or otherwise) of corresponding mathematical models and simulations. We were specifically interested in whether the models could shed light on any of the fundamental mechanisms underlying this disease. Moreover, we were aiming to form a new community of clinicians and modelers looking at this disease and to define a common language and theoretical framework within which collaboration could flourish. The workshop showed the role that models can play, not just in trying to fit to existing data or predicting what individual mechanisms or system behaviors might occur, but also in challenging the orthodoxy of the concept of a stem cell and concepts such as "differentiation" and "determination". For years the prevailing view of a stem cell has been an entity (object) with a fixed set of behaviors and with a pre-determined fate. New perspectives in modeling, coupled with the new data that are being accumulated in the genesis of CML and its treatment, questions these assumptions. We propose how we can reach a consensus about a functional view of stem cells in a more continuous and flexible way and how, within this context, we can investigate the significance of modeling results and how they might impact on our interpretation of experimental observations and the development of new clinical strategies. This paper reports on the workshop and the state-of-the-art models and data from experimental and clinical trials, and sets out a roadmap for more interdisciplinary collaboration between modelers, wet-lab experimentalists, and clinicians interested in CML. It is our strong belief that a more integrated and coherent interdisciplinary approach will further advance the treatment of CML in future years.