This phase II trial studies how well durvalumab and tremelimumab work in treating
participants with ovarian, primary peritoneal, or fallopian tube cancer that has come back or
does not respond to treatment. Immunotherapy with monoclonal antibodies, such as durvalumab
and tremelimumab, may help the body's immune system attack the cancer, and may interfere with
the ability of tumor cells to grow and spread. It is not yet known whether give durvalumab
and tremelimumab in combination or sequential administration works better in treating
participants with ovarian, primary peritoneal, or fallopian tube cancer.