Immune checkpoint therapy is one of the most promising immunotherapeutic methods that are likely able to give rise to durable treatment response for various cancer types. Despite much progress in the past decade, there are still critical open questions with particular regards to quantifying and predicting the efficacy of treatment and potential optimal regimens for combining different immune-checkpoint blockades. To shed light on this issue, here we develop clinically-relevant, dynamical systems models of cancer immunotherapy with a focus on the immune checkpoint PD-1/PD-L1 blockades. Our model allows the acquisition of adaptive immune resistance in the absence of treatment, whereas immune checkpoint blockades can reverse such resistance and boost anti-tumor activities of effector cells. Our numerical analysis predicts that anti-PD-1 agents are commonly less effective than anti-PD-L1 agents for a wide range of model parameters. We also observe that combination treatment of anti-PD-1 and anti-PD-L1 blockades leads to a desirable synergistic effect. Our modeling framework lays the ground for future data-driven analysis on combination therapeutics of immune-checkpoint treatment regimes and thorough investigation of optimized treatment on a patient-by-patient basis.