This is a 3-part phase 1-2 study in patients with anaplastic lymphoma kinase (ALK) + or other potentially crizotinib-sensitive NSCLC who have been receiving crizotinib. Part A is a single-arm, Phase 1, open-label, dose escalation design in patients with NSCLC who have already been receiving crizotinib for at least 8 weeks and continue to tolerate therapy. Part B is a Phase 2, open-label, randomized continuation design comparing crizotinib alone versus the combination of crizotinib + AT13387 at the maximum tolerated dose established in Part A. Part C is an open-label, randomized, Phase 2, Simon's 2 stage design evaluating single agent AT13387 or combination AT13387 + crizotinib at the MTD established in Part A in patients who progressed on crizotinib at any time.