This is an open-label, multi-center study to determine the efficacy and safety of tremelimumab in the treatment of different cohorts of patients with selected advanced solid tumors. If eligible and at the discretion of the Investigator, after confirmed disease progression on tremelimumab monotherapy or during follow-up, patients will have the option of being sequenced to MEDI4736 (MedImmune 4736) monotherapy or MEDI4736 + tremelimumab combination therapy, for up to 12 months or until disease progression, whichever comes sooner.