The malignant tumor is a complex heterogeneous set of cells functioning in a no less heterogeneous microenvironment. Like any dynamic system, cancerous tumors evolve and undergo changes in response to external influences, including therapy. Initially, most tumors are susceptible to treatment. However, remaining cancer cells may rapidly reestablish the tumor after a temporary remission. These new populations of malignant cells usually have increased resistance not only to the first-line agent, but also to the second- and third-line drugs, leading to a significant decrease in patient survival. Multiple studies describe the mechanism of acquired therapy resistance. In past decades, it became clear that, in addition to the simple selection of pre-existing resistant clones, therapy induces a highly complicated and tightly regulated molecular response that allows tumors to adapt to current and even subsequent therapeutic interventions. This review summarizes mechanisms of acquired resistance, such as secondary genetic alterations, impaired function of drug transporters, and autophagy. Moreover, we describe less obvious molecular aspects of therapy resistance in cancers, including epithelial-to-mesenchymal transition, cell cycle alterations, and the role of intercellular communication. Understanding these molecular mechanisms will be beneficial in finding novel therapeutic approaches for cancer therapy.