Main Inclusion Criteria

          -  Histologically-confirmed hematologic malignancy that is expected to express CD20
             (Relapsed after or refractory to respond to at least one prior treatment regimen; no
             available treatment options that are expected to prolong survival or patients refusing
             chemotherapy or autologous stem cell transplant (SCT). Note: The expansion part is
             restricted to relapsed/refractory follicular lymphoma (r/r FL) and relapsed/refractory
             diffuse large B cell lymphoma (r/r DLBCL))

          -  At least one measurable target lesion

          -  Fresh pre-treatment biopsy, but if this cannot be taken, a previous archived biopsy
             from metastatic lesion can be taken as replacement if it is not older than 6 months
             and not confounded by major events (progression, treatment)

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          -  Adequate organ function (liver, hematological, renal)

          -  Negative test results for hepatitis B virus (HBV), hepatitis C virus (HCV), and human
             immunodeficiency virus (HIV)

        Inclusion Criteria Specific to Imaging Substudy

          -  At least two measurable target lesions

          -  Able to provide two fresh tumor biopsies (baseline and on-treatment)

        Main Exclusion Criteria

          -  Participants with Chronic Lymphocytic Leukemia (CLL), acute lymphoblastic leukemia
             (ALL), lymphoblastic lymphoma, Richter's transformation, CD20-positive ALL, Burkitt
             lymphoma, or lymphoplasmacytic lymphoma

          -  Current > Grade 1 peripheral neuropathy (only for participants being treated in the
             polatuzumab vedotin arm)

          -  Patients with known active infection, or reactivation of a latent infection within 4
             weeks prior to Obinutuzumab (Gpt) infusion

          -  Patient with history of confirmed progressive multifocal leukoencephalopathy (PML)

          -  History of leptomeningeal disease

          -  Current or past history of central nervous system (CNS) lymphoma

          -  Current or past history of CNS disease

          -  Major surgery or significant traumatic injury </=28 days prior to Gpt infusion

          -  Significant cardiovascular disease or significant pulmonary disease

          -  Active or history of autoimmune disease or immune deficiency (with exceptions, e.g.
             hypothyroidism and Diabetes mellitus Type 1)

          -  History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g. bronchiolitis
             obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of
             active pneumonitis on screening chest computed tomography (CT) scan

          -  Treatment with any other standard anti-cancer radiotherapy / chemotherapy including
             investigational therapy within 4 weeks prior to Gpt infusion

          -  Prior solid organ transplantation

          -  Prior allogenic stem cell transplant (SCT)

          -  Autologous SCT within 100 days prior to Gpt infusion

          -  Documented refractoriness to an obinutuzumab-monotherapy regimen

          -  Prior treatment with targeted therapies and systemic
             immunotherapeutic/immunostimulating agents within 4 weeks or 5 half-lives of the drug,
             whichever is shorter, prior to Gpt infusion

          -  Any history of immune related >/= Grade 3 adverse events (AE) with the exception of
             endocrinopathy managed with replacement therapy

          -  Ongoing corticosteroid use >25 milligrams/day of prednisone or equivalent within 4
             weeks prior to and during study treatment

          -  Treatment with systemic immunosuppressive medication

          -  Administration of a live, attenuated vaccine within 4 weeks prior to Gpt infusion or
             anticipation that such a live attenuated vaccine will be required during the study or
             within 5 months after last dose of study treatment

        Exclusion Criteria Specific to Imaging Substudy

          -  Circulating lymphoma cells, defined by out of range (high) absolute lymphocyte count
             and/or the presence of abnormal/malignant cells in the peripheral blood differential
             signifying circulating lymphoma cell

          -  Participants who have had splenectomy or functional asplenia that could compromise
             protocol objectives