Differences between normal adult tissue stem cells and cancer stem/initiating cells remain poorly defined. For example, it is controversial if cancer stem cells can become fully quiescent, require a stem cell niche, are better at repairing DNA damage than the bulk of the cancer cells, and if and how they regulate symmetric versus asymmetric cell divisions. This minireview will not only provide our personal views to address some of these outstanding questions, but also present evidence that an understanding of telomere dynamics and telomerase activity in normal and cancer stem cells may provide additional insights into how tumors are initiated, and how they should be monitored and treated.