This is a multicenter, open-label, Phase 1b study of atezolizumab (anti-programmed death-ligand 1 [anti-PD-L1] monoclonal antibody) in participants who have hypomethylating agent (HMA)-naïve myelodysplastic syndromes (MDS) and are International Prognostic Scoring System-Revised (IPSS-R) intermediate/high/very high-risk, or have MDS relapsed or are refractory (R/R) to prior HMA therapy. The primary objectives of this study are to determine the safety and tolerability of atezolizumab therapy in these participant populations, including treatment in combination with azacitidine.