Synthetic polymer nanocomposites display enhanced toughness and energy absorption with regard to unreinforced polymers. The interaction between the polymeric matrix and the reinforcements triggers failure mechanisms such as fiber fracture, crack deflection, among others. Biological nanocomposites sometimes exhibit higher toughness than synthetic nanocomposites due to their hierarchical organization. This arrangement triggers failure modes such as mineral bridging and delamination. This review summarizes and classifies systematically the failure mechanisms involved in these nanocomposites. These failures modes are compared for a better understanding and to provide new design criteria for the development of novel bioinspired polymer nanocomposites with enhanced mechanical properties.