This multi-center, open-label study will evaluate the safety, pharmacokinetics, pharmacodynamics and preliminary efficacy of vanucizumab as a single agent or in combination with atezolizumab in participants with locally advanced or metastatic solid tumors. Cohorts of participants will receive escalating doses of vanucizumab, fixed dose of vanucizumab (MTD and/or recommended phase two dose [RP2D]), and fixed dose of vanucizumab in combination with atezolizumab, intravenously every 2 weeks.

Inclusion Criteria:

• Participants with histologically confirmed epithelial ovarian, fallopian tube or primary peritoneal cancer
• Participants must have platinum resistant disease defined as progression within <6 months from completion of a minimum of 4 platinum therapy cycles OR Participants must have platinum refractory disease, which is defined as progression during platinum based chemotherapy
• Less than or equal to (<=) 2 prior lines of systemic therapy
• The participant is willing to consent to and undergo a pre-treatment and on treatment core or excisional biopsy of the tumor
• Measurable disease as determined by RECIST 1.1
• Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• Adequate hematological function
• Adequate liver function
• Adequate renal function
• Adequate coagulation
• Adequate cardiovascular function
• Recovery from all reversible adverse events of previous anti-cancer therapies to baseline or Common Terminology Criteria for Adverse Events (CTCAE) Grade (G) 1, except for alopecia (any grade) and <= G 2 sensory peripheral neuropathy

Exclusion Criteria:

• Participants with primary central nervous system (CNS) tumors or CNS tumor involvement. Participants with metastatic CNS tumors may participate in this trial under conditions defined by protocol
• Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 1 of Cycle 1, or abdominal surgery, abdominal interventions or significant abdominal traumatic injury within 60 days prior to Day 1 of Cycle 1 or anticipation of the need for major surgical procedure during the course of the study or non-recovery from side effects of any such procedure
• Significant cardiovascular/cerebrovascular disease within 6 months prior to study drug administration
• Known human immuno deficiency virus (HIV) infection or known active hepatitis B or hepatitis C virus infection or active tuberculosis
• Participants previously treated with vascular endothelial growth factor (VEGF)-A inhibitors and with agents targeting Angiopoietin (Ang)-1/2 and/or Tyrosine-protein kinase receptor2
• History of intra-abdominal inflammatory process within the last 12 months such as, but not limited to, diverticulitis, peptic ulcer disease, or colitis
• Any prior radiotherapy to the pelvis or abdomen
• Treatment with systemic immunostimulatory agents, including but not limited to, interferon (IFN)-alpha, IFN-beta, interleukin (IL)-2, conjugated IL-2 cytokines within 6 weeks or five half-lives of the drug, whichever is longer, prior to screening
• History of bowel obstruction and/or clinical signs or symptoms of gastro-intestinal obstruction, including sub-occlusive disease related to the underlying disease (however, participants with signs/symptoms of sub/occlusive syndrome/bowel obstruction at the time of initial diagnosis may be enrolled if they had received definitive [surgical] treatment for symptom resolution). History of abdominal fistula or tracheo-oesophageal fistula, gastrointestinal perforation or intra-abdominal abscess, unless occurred and resolved before initial diagnosis and unrelated to the underlying cancer disease. Evidence of recto-sigmoid involvement by pelvic examination or bowel involvement on Computed tomography (CT)
• Chronic daily treatment with non-steroidal anti-inflammatory drug (NSAID) (occasional use for the symptomatic relief of medical conditions, for example, headache, fever is allowed)
• Treatment with systemic immunosuppressive medications including, but not limited, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents within 2 weeks prior to study drug administration
• Previous treatment with checkpoint inhibitors (e.g. anti Programmed death [PD]-1, anti-PD-ligand 1, anti Cytotoxic T-lymphocyte-associated molecule-4) or prior treatment with cluster of differentiation (CD) 137 agonists or any other antibody or drug targeting T cell co-stimulation or other immune checkpoint blockade therapies
• History of autoimmune disease including, but not limited to systemic lupus erythematosus (SLE), Sjögren's syndrome, glomerulonephritis, multiple sclerosis, rheumatoid arthritis, vasculitis, systemic immune activation, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Guillain-Barré syndrome, Bell's palsy
• History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g. bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest CT scan
• Prior allogeneic bone marrow transplantation or prior solid organ transplantation
• Administration of a live, attenuated vaccine within 4 weeks before Cycle1 Day1 or anticipation that such a live attenuated vaccine will be required during the study