Aneuploid cells are frequently observed in human tumors, suggesting that aneuploidy may play an important role in the development of cancer. In this review, I discuss the processes that may give rise to aneuploid cells in normal tissue and in tumors. Aneuploid cells may arise directly from diploid cells through errors in chromosome segregation, as a consequence of incorrect microtubule-kinetochore attachments, or through failure of the spindle checkpoint. A second route to formation of aneuploid cells is through a tetraploid intermediate, where division of tetraploid cells can yield very high rates of chromosome missegregation as a consequence of multipolar spindle formation. Diploid cells may become tetraploid through a variety of mechanisms, including endoreduplication, cell fusion, and cytokinesis failure. Although aneuploid cells may arise from either diploid or tetraploid cells, the fate of the resulting aneuploid cells may be distinct. It is therefore important to understand the different pathways that can give rise to aneuploid cells, and how the varied origins of these cells affect their subsequent ability to survive or proliferate.