This is a phase 1B, multi-center, dose-finding study of glofitamab administered in combination with obinutuzumab (Gazyva; [G]), rituximab (R) and standard doses of CHOP (G/R-CHOP or R-CHOP) in participants with r/r NHL and G/R CHOP or Pola-R-CHP in participants with untreated diffuse large B-cell lymphoma (DLBCL). Evaluating the safety, preliminary activity, pharmacokinetic (PK), and pharmacodynamic effects of this combination will be the main objectives of this study. The study is divided in two parts:

• Part I: Dose finding in participants with r/r NHL; test use of G vs R in Cycle 1
• Part II: Dose Expansion. The maximum tolerated dose or optimal biological dose (MTD or OBD) will be further assessed in participants with untreated DLBCL (>18 years of age with an age-adjusted International Prognostic Index (IPI) of 2-5). Glofitamab will be studied in combination with R-CHOP and Pola-R-CHP.

Inclusion Criteria:

• Age >/=18 years
• For Part I r/r NHL dose-escalation, and Part II r/r NHL expansion: Histologically-confirmed NHL that is expected to express CD20, and which has relapsed/progressed following at least one prior treatment regimen containing R or G. Participants must be appropriate for treatment with CHOP and typically should not have been exposed to prior anthracyclines or must not exceed the cumulative lifetime dose of anthracyclines
• For Part II untreated DLBCL expansion: Histologically confirmed previously-untreated DLBCL that is expected to express CD20
• Able to provide a pretreatment biopsy between the final dose of last prior therapy and initiation of study medication at Cycle 1/Day 1
• Measurable disease, defined as at least one bi-dimensionally measurable nodal lesion, defined as >1.5 cm in its longest dimension, or at least one bi-dimensionally measurable extranodal lesion, defined as >1.0 cm in its longest dimension.
• Participants must have at least one measurable target lesion (> or = 1.5 cm) in its largest dimension by computed tomography (CT) scan
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 for participants with r/r NHL; ECOG performance status 0-3 for participants with untreated DLBCL
• Life expectancy (in the opinion of the Investigator) of 18 weeks
• Adverse events (AEs) from prior anti-cancer therapy must have resolved to Grade </= 1
• Adequate liver function
• Adequate hematological function
• Adequate renal function
• Negative serologic or polymerase chain reaction (PCR) test results for acute or chronic hepatitis B virus (HBV) infection
• Negative test results for hepatitis C virus (HCV) and human immunodeficiency virus (HIV)

Exclusion Criteria:

• Inability to comply with protocol mandated hospitalization and restrictions
• Participants with known active infection, or reactivation of a latent infection, whether bacterial, viral (including, but not limited to Epstein Barr virus (EBV), cytomegalovirus (CMV), HBV, HCV, and HIV), fungal, mycobacterial, or other pathogens (excluding fungal infections of nail beds) or any major episode of infection requiring hospitalization or treatment with IV antibiotics (for IV antibiotics, this pertains to completion of last course of antibiotic treatment) within 4 weeks of dosing
• Prior treatment with systemic immunotherapeutic agents, including, but not limited to, radioimmuno-conjugates, antibody-drug conjugates, immune/cytokines, and monoclonal antibodies (e.g., anti-CTLA4, anti-PD1, and anti-PDL1) within 4 weeks or five half-lives of the drug, whichever is shorter, before G- or R-CHOP or Pola-R-CHP infusion on Cycle 1/Day 1
• Current Grade > 1 peripheral neuropathy by clinical examination or demyelinating form of Charcot-Marie-Tooth disease (only for participants treated in the polatuzumab vedotin arm)
• History of treatment-emergent immune-related AEs associated with prior immunotherapeutic agents, as follows: Grade >/=3 AEs, with the exception of Grade 3 endocrinopathy managed with replacement therapy; Grade 1-2 AEs that did not resolve to baseline after treatment completion
• Contraindication to any of the individual components of the immunochemotherapy
• Treatment with standard radiotherapy, any chemotherapeutic agent, or treatment with any other investigational anti-cancer agent within 4 weeks prior to study treatment at Cycle 1/Day 1 infusion
• Prior solid organ transplantation
• Prior allogeneic stem cell transplantation
• Autologous stem cell transplantation within 100 days prior to Cycle 1/Day 1
• Prior treatment with CAR T-cell therapy within 30 days prior to study treatment at Cycle 1 Day 1
• History of autoimmune disease
• History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibody therapy (or recombinant antibody-related fusion proteins)
• A history of confirmed progressive multifocal leukoencephalopathy
• Current or past history of central nervous system (CNS) lymphoma
• Ongoing corticosteroid use > 30 mg/day of prednisone or equivalent. Participants who received corticosteroid treatment with \