This is a Phase 1b/2, open label, multicenter, safety and clinical activity study of avelumab in combination with chemotherapy as first-line treatment of adult patients with locally advanced or metastatic solid tumors. Initially, avelumab will be evaluated in combination with pemetrexed and carboplatin in patients with advanced non-squamous non-small cell lung cancer (NSCLC) (Cohort A1) and in combination with gemcitabine and cisplatin in patients with cisplatin-eligible urothelial (bladder) cancer (UC) (Cohort A2). As more information is learned about other anti-cancer immunotherapy agents, in future portions of the study, avelumab may be combined with chemotherapy and other anti-cancer immunotherapy agents in patients with these same or different tumor types.