Patient description: A Pap smear in a 54-year-old woman revealed abnormal cervical squamous intraepithelial/glandular lesion. She tested positive for HPV 16. She is sexually active with her husband and has 4 children. She is menopausal and uses no contraception. She smokes and drinks alcohol frequently. She is otherwise healthy. She was offered conization.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Appendix Adenocarcinoma Human Papillomavirus-Related Anal Squamous Cell Carcinoma Human Papillomavirus-Related Cervical Squamous Cell Carcinoma Human Papillomavirus-Related Squamous Cell Carcinoma of the Penis Human Papillomavirus-Related Vulvar Squamous Cell Carcinoma Neuroendocrine Carcinoma Pancreatic Neuroendocrine Tumor Recurrent Merkel Cell Carcinoma Recurrent Nasopharynx Carcinoma Recurrent Peritoneal Malignant Mesothelioma Recurrent Pleural Malignant Mesothelioma Stage III Merkel Cell Carcinoma AJCC v7 Stage III Nasopharyngeal Carcinoma AJCC v7 Stage III Pleural Malignant Mesothelioma AJCC v7 Stage IV Merkel Cell Carcinoma AJCC v7 Stage IV Nasopharyngeal Carcinoma AJCC v7 Stage IV Pleural Malignant Mesothelioma AJCC v7 Stage IVA Nasopharyngeal Carcinoma AJCC v7 Stage IVB Nasopharyngeal Carcinoma AJCC v7 Stage IVC Nasopharyngeal Carcinoma AJCC v7 Vaginal Squamous Cell Carcinoma, Not Otherwise Specified Signed informed consent form Ability to comply with the study protocol, in the investigator's judgment Measurable disease according to Response Evaluation in Solid Tumors (RECIST) version (v) 1.1; previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation; the pleural mesothelioma cohort will require measurable disease according to modified Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 Absolute neutrophil count (ANC) >= 1.5 x 10^9/L without granulocyte colony-stimulating factor support, obtained within 14 days prior to initiation of study treatment Lymphocyte count >= 0.5 x 10^9/L, obtained within 14 days prior to initiation of study treatment Platelet count >= 100 x 10^9/L without transfusion, obtained within 14 days prior to initiation of study treatment White blood cell (WBC) count >= 2500/ul, obtained within 14 days prior to initiation of study treatment Hemoglobin >= 90 g/L (patients may be transfused to meet this criterion), obtained within 14 days prior to initiation of study treatment Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and alkaline phosphatase (ALP) =< 2.5 x upper limit of normal (ULN), obtained within 14 days prior to initiation of study treatment, with the following exceptions: patients with documented liver metastases: AST and ALT =< 5 x ULN; patients with documented liver or bone metastases: alkaline phosphatase (ALP) =< 5 x ULN  Treatment for the studied cancer within 28 days prior to initiation of study treatment Treatment with investigational therapy within 28 days prior to initiation of study treatment History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins Known hypersensitivity to biopharmaceutical agents produced in Chinese hamster ovary cells Known allergy or hypersensitivity to any component of the atezolizumab formulation Known allergy or hypersensitivity to any component of the bevacizumab formulation Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjogren's syndrome, Guillain-Barre syndrome, or multiple sclerosis, with the following exceptions: patients with a history of autoimmune-related hypothyroidism who are on thyroid replacement hormone are eligible for the study; patients with controlled type 1 diabetes mellitus who are on an insulin regimen are eligible for the study; patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met Rash must cover < 10% of body surface area Disease is well controlled at baseline and requires only low-potency topical corticosteroids No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids within the previous 12 months