Inclusion Criteria:

* Patients must have histologic documentation of well-differentiated or moderately differentiated neuroendocrine tumor from either a primary or metastatic site

* If different histologic classification schemes are used, equivalent histologic classifications (for example "grade 1", "low-grade", or "intermediate-grade") are allowed
* Patients with poorly differentiated neuroendocrine carcinoma or small cell carcinoma are excluded
* Documentation from a metastatic disease site is sufficient if there is clinical evidence of a pancreatic primary site
* Locally unresectable or metastatic disease
* Patients must have either histologic documentation of a pancreatic primary site, or clinical evidence of a pancreatic neuroendocrine primary tumor as determined by the treating physician

* Patients with neuroendocrine tumors (e.g., gastrinoma, VIPoma) in whom a pancreatic or peripancreatic primary site is strongly suspected are also eligible
* Patients must have evidence of disease (measurable or non-measurable) with evidence of progression within the past 12 months
* Measurable disease:

Lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as >= 2 cm with conventional techniques or as >= 1 cm with spiral computed tomography (CT) scan

* Non-measurable disease:

All other lesions, including small lesions (longest diameter < 20 mm with conventional techniques or < 10 mm with spiral CT scan) and truly non-measurable lesions; lesions that are considered non-measurable include the following:

* Bone lesions
* Leptomeningeal disease
* Ascites
* Pleural/pericardial effusion
* Inflammatory breast disease
* Lymphangitis cutis/pulmonis
* Abdominal masses that are not confirmed and followed by imaging techniques
* Cystic lesions

* No prior treatment with bevacizumab, everolimus, or other mammalian target of rapamycin (mTOR) inhibitors
* Other prior treatments, including but not limited to prior cytotoxic chemotherapy, alpha interferon, tyrosine kinase inhibitors, external beam radiation therapy, and radiopeptide therapy are allowed
* There is no limit on the number of prior treatment regimens
* Any prior treatment (with the exception of octreotide) must be completed at least 4 weeks prior to initiation of treatment

* Prior treatment with embolization or ablative therapies is allowed if measurable disease remains outside of the treated area
* There is no limit on the prior number of procedures

* Treatment with somatostatin analogs is a requirement of the study
* Patients receiving octreotide at the time of study entry may continue at the same dose level for the duration of the study
* Patients not receiving octreotide will initiate treatment according to study guidelines
* Prior progression on somatostatin analogs or a negative octreotide scan does not exclude patient participation in this study

* Patients should have completed any major surgery >= 4 weeks from start of treatment
* Patients must have completed any minor surgery >= 2 weeks prior to start of treatment
* Patients must have fully recovered from the procedure
* Insertion of a vascular access device is not considered major or minor surgery

* Patients should not receive immunization with attenuated live vaccines within one week prior to registration or during protocol therapy
* No concurrent condition resulting in immune compromise, including chronic treatment with corticosteroids or other immuno suppressive agents
* No active or severe liver disease (e.g., acute or chronic hepatitis, cirrhosis); no positive anti-hepatitis B virus (HBV); HBV seropositive patients (hepatitis B surface antigen \[HBsAg\] positive) are eligible if they are closely monitored for evidence of active HBV infection by HBV deoxyribonucleic acid (DNA) testing, and they agree to receive suppressive therapy with lamivudine or other HBV-suppressive therapy until at least 4 weeks after the last dose of everolimus; patients who are hepatitis C antibody positive are eligible provided that hepatitis C viral load (hepatitis C ribonucleic acid \[RNA\]) is undetectable
* No clinical evidence of brain metastases or carcinomatous meningitis
* No history of gastrointestinal (GI) perforation within 12 months prior to registration
* No history of clinically significant bleeding episodes
* Patients on therapeutic anticoagulation are eligible for the study provided that they are on a stable dose of anticoagulants
* No uncontrolled diabetes mellitus
* Patients with a history of severely impaired lung function as defined as spirometry and diffusing capacity of the lung for carbon monoxide (DLCO) that is 50% of the normal predicted value and/or oxygen (O2) saturation that is 88% or less at rest on room air are excluded
* Patients with fasting serum cholesterol >= 300 mg/dL OR >= 7.75 mmol/L AND fasting triglycerides >= 2.5 X upper limit of normal (ULN) should initiate lipid-lowering medications with the goal of achieving levels below these thresholds
* No history of intolerance or allergies to octreotide
* Patients with a history of hypertension must be adequately controlled (baseline blood pressure \[BP\] < 150/90 mm Hg) on antihypertensives
* No current congestive heart failure (New York Heart Association class II, III, or IV)
* No symptomatic arterial peripheral vascular disease
* No history of aortic aneurysm, aortic dissection, angina, myocardial infarction, stroke, or other arterial thrombotic events within 6 months of registration
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1
* Women must not be pregnant or lactating; both men and women of childbearing potential must be advised of the importance of using effective birth control measures during the course of the study
* Granulocytes >= 1,500/uL
* Platelets >= 100,000/uL
* Creatinine =< 1.5 x upper limit of normal
* Bilirubin =< 1.5 x upper limit of normal
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 2.5 x upper limit of normal (=< 5 x upper limit of normal if liver metastases present)
* Urine protein =< 1+ OR urine creatinine ratio =< 1 (by urinalysis)
* If urine protein creatinine (UPC) ratio is > 1 on urinalysis, then 24-hour urine collection for protein must be obtained and level must be < 1,000 mg for patient enrollment