Antibody-drug conjugates (ADCs) combine the tumor selectivity of antibodies with the potency of cytotoxic small molecules thereby constituting antibody-mediated chemotherapy. As this inherently limits the adverse effects of the chemotherapeutic, such approaches are heavily pursued by pharma and biotech companies and have resulted in four FDA (Food and Drug Administration)-approved ADCs. However, as with other cancer therapies, durable responses are limited by the fact that under cell stress exerted by these drugs, tumors can acquire mechanisms of escape. Resistance can develop against the antibody component of ADCs by down-regulation/mutation of the targeted cell surface antigen or against payload toxicity by up-regulation of drug efflux transporters. Unique resistance mechanisms specific for the mode of action of ADCs have also emerged, like altered internalization or cell surface recycling of the targeted tumor antigen, changes in the intracellular routing or processing of ADCs, and impaired release of the toxic payload into the cytosol. These evasive changes are tailored to the specific nature and interplay of the three ADC constituents: the antibody, the linker, and the payload. Hence, they do not necessarily endow broad resistance to ADC therapy. This review summarizes preclinical and clinical findings that shed light on the mechanisms of acquired resistance to ADC therapies.