Activating gene rearrangements of anaplastic lymphoma kinase (ALK) have been identified as driver mutations in non‐small‐cell lung cancer, inflammatory myofibroblastic tumors, and other cancers. Crizotinib, a dual MET/ALK inhibitor, has demonstrated promising clinical activity in patients with non‐small‐cell lung cancer and inflammatory myofibroblastic tumors harboring ALK translocations. Inhibitors of driver kinases often elicit kinase domain mutations that confer resistance, and such mutations have been successfully predicted using in vitro mutagenesis screens. Here, this approach was used to discover an extensive set of ALK mutations that can confer resistance to crizotinib. Mutations at 16 residues were identified, structurally clustered into five regions around the kinase active site, which conferred varying degrees of resistance. The screen successfully predicted the L1196M, C1156Y, and F1174L mutations, recently identified in crizotinib‐resistant patients. In separate studies, we demonstrated that crizotinib has relatively modest potency in ALK‐positive non‐small‐cell lung cancer cell lines. A more potent ALK inhibitor, TAE684, maintained substantial activity against mutations that conferred resistance to crizotinib. Our study identifies multiple novel mutations in ALK that may confer clinical resistance to crizotinib, suggests that crizotinib’s narrow selectivity window may underlie its susceptibility to such resistance and demonstrates that a more potent ALK inhibitor may be effective at overcoming resistance. A mutagenesis screen identified multiple mutations in the kinase domain that confer resistance to the first generation ALK inhibitor crizotinib. Our studies suggest that crizotinib’s low potency and narrow selectivity window for ALK may underlie its susceptibility to such resistance. These results provide guidance for the rational design and optimization of potent and selective second generation drugs that may be able to overcome ALK‐based mechanisms of resistance.