Recently, there has been a coordinated effort from academic institutions and the pharmaceutical industry to identify biomarkers that can predict responses to immune checkpoint blockade in cancer. Several biomarkers have been identified; however, none has reliably predicted response in a sufficiently rigorous manner for routine use. Here, we argue that the therapeutic response to immune checkpoint blockade is a critical state transition of a complex system. Such systems are highly sensitive to initial conditions, and critical transitions are notoriously difficult to predict far in advance. Nevertheless, warning signals can be detected closer to the tipping point. Advances in mathematics and network biology are starting to make it possible to identify such warning signals. We propose that these dynamic biomarkers could prove to be useful in distinguishing responding from non-responding patients, as well as facilitate the identification of new therapeutic targets for combination therapy.