This is a phase II, multi-center, open-label, five-arm study in which the efficacy and safety of oral ceritinib treatment will be assessed in patients with NSCLC metastatic to the brain and/or to leptomeninges harboring a confirmed ALK rearrangement, using the FDA approved Vysis ALK Break Apart FISH Probe Kit (Abbott Molecular Inc.) test and scoring algorithm (including positivity criteria). If documentation of ALK rearrangement as described above is not locally available, a test to confirm ALK rearrangement must be performed by a Novartis designated central laboratory. Patients must wait for the central laboratory result of the ALK rearrangement status before initiating treatment with ceritinib.