Chemo-resistance and radio-resistance are a major cause of recurrence and progression of many cancers, regardless of improvements in therapies. Since cancer stem cells (CSCs) were identified as a rare population with the abilities of self-renewal; tumor initiation; aberrant differentiation, which contributes to tumor heterogeneity; and resistance to anticancer therapeutics, they have been considered a major cause of tumor recurrence post-therapy and a primary therapeutic target in relapse prevention. A number of studies have demonstrated the mechanisms underlying chemo-resistance and radio-resistance of CSCs. In this review, we describe intrinsic and extrinsic factors underlying CSC chemo-resistance and radio-resistance. The intrinsic factors regulate CSC signaling pathways involved in stem cell signaling, anti-apoptotic pathways, ABC transporter expression, and DNA damage repair systems. The extrinsic factors include the resistance mechanisms resulting from the interactions between CSCs and the microenvironment composed of vessels, fibroblasts, immune cells, extracellular matrix, and diverse soluble factors. Furthermore, we introduce diverse therapeutic agents used in experimental or clinical trials to target CSCs. Understanding how CSCs acquire resistance to anticancer therapeutics will give us opportunity to develop improved therapeutic approaches.