Chronic myeloid leukemia (CML) is a clonal myeloproliferative neoplasia associated with the t(9,22)(q34:q11) reciprocal translocation, also known as Philadelphia chromosome (Ph). As a result of such abnormality, a chimeric gene (bcr-abl) is produced that is translated into a chimeric protein (BCR-ABL), a constitutively activated tyrosine kinase. Major cell dysfunctions result from this abnormal kinase activity, including increased proliferation and reduced apoptosis. Based on the structure of BCR-ABL, several molecules have been designed that inhibit its kinase activity. Five such molecules have already been brought into the clinic for the treatment of Ph+ CML patients. Good results have been obtained in terms of patients' remission rates and quality of life. Some major problems, however, have been observed. Firstly, a significant proportion of patients develop resistance to the drugs; secondly, it is clear that such drugs affect most of the leukemic cells, but do not eliminate leukemia stem cells. Thus, important CML-related challenges remain to be solved in the near future.