Aging is associated with a marked increase in a number of diseases, including many types of cancer. Due to the complex and multi-factorial nature of both aging and cancer, accurate deciphering of causative links between aging and cancer remains a major challenge. It is generally accepted that initiation and progression of cancers are driven by a process of clonal evolution. In principle, this somatic evolution should follow the same Darwinian logic as evolutionary processes in populations in nature: diverse heritable types arising as a result of mutations are subjected to selection, resulting in expansion of the fittest clones. However, prevalent paradigms focus primarily on mutational aspects in linking aging and cancer. In this review, we will argue that age-related changes in selective pressures are likely to be equally important. We will focus on aging-related changes in the hematopoietic system, where age-associated alterations are relatively well studied, and discuss the impact of these changes on the development of leukemias and other malignancies.