A Study of Atezolizumab Administered Alone or in Combination With Azacitidine in Participants With Myelodysplastic Syndromes

Inclusion Criteria:

* Diagnosis of MDS (participants with therapy-related MDS are eligible)
* Eastern Cooperative Oncology Group (ECOG) performance status score less than or equal to (\</=) 2
* Adequate end-organ function, as determined by laboratory tests obtained within 28 days prior to the first dose of study drug
* Willing and able to undergo a pre-treatment bone marrow biopsy and subsequent on-treatment bone marrow biopsies
* Women who are not postmenopausal or surgically sterile must have a negative serum pregnancy test result within 28 days prior to initiation of study drug
* For women of childbearing potential and men: agreement to remain abstinent (refrain from heterosexual intercourse) or use highly effective contraceptive measures

For participants in Cohorts A, A2, B, and B2:

* Progression at any time after initiation of azacitidine or decitabine treatment OR
* Failure to achieve complete or partial response or hematological improvement after at least six 4-week cycles of azacitidine or either four 4-week or four 6-week cycles of decitabine OR
* Relapse after initial complete or partial response or hematological improvement after six 4-week cycles of azacitidine or either four 4-week or four 6-week cycles of decitabine administered within the past 2 years

For participants in Cohorts C1 and C2:

* Must not have received prior treatment for MDS with any hypomethylating agent
* IPSS-R risk category of Intermediate, High, or Very High assessed at screening

Exclusion Criteria:

* Participants with a diagnosis of MDS secondary to paroxysmal nocturnal hemoglobinuria (PNH), aplastic anemia, or another inherited bone marrow failure disorder
* Prior allogeneic stem cell transplant or solid organ transplant
* Pregnant or lactating, or intending to become pregnant during the study
* Investigational therapy within 28 days prior to initiation of study treatment
* Immunosuppressive therapy within 6 weeks of Cycle 1, Day 1
* Prior treatment with immune checkpoint blockade therapies (anti-cytotoxic T-lymphocyte-associated protein 4 \[CTLA-4\], anti-programmed death-1 \[PD-1\] or anti-PD-L1) or immune agonists (anti-cluster of differentiation \[CD\] 137, anti-CD40, anti-OX40)
* Any other therapy or serious medical condition, as specified in the protocol, or abnormality in clinical laboratory tests that, in the investigator's judgement, precludes the participant's safe participation in and completion of the study
* Left ventricular ejection fraction (LVEF) \</= 40 percent (%) at screening
* Planned major surgery during the study or within 4 weeks of Cycle 1, Day 1
* History of idiopathic pulmonary fibrosis, organizing pneumonitis, drug-induced pneumonitis, or idiopathic pneumonitis or evidence of active pneumonitis on screening chest computed tomography (CT) scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted.