Antibody-drug conjugates (ADCs) are designed to specifically bind to and kill cells expressing their target antigens. In addition to the obvious requirement of the presence of the target antigen on the cell surface, several other factors contribute to the sensitivity of target cells to the action of ADCs. These include (i) the rate of internalization of the ADC, (ii) its proteolytic degradation in late endosomes and lysosomes and the subsequent release of cytotoxic drug, and (iii) the intracellular concentration of the released drug. In addition to killing antigen-expressing cells, some ADCs were found to kill bystander cells irrespective of their antigen expression. This review summarizes the current knowledge of the mechanisms of killing of antigen-expressing and bystander cells by antibody-drug conjugates.