Designing and debugging distributed systems is notoriously difficult. The correctness of a distributed system is largely determined by its handling of failure scenarios. The sequence of events leading to a bug can be long and complex, and it is likely to include message reorderings and failures. On single-node systems, interactive debuggers enable stepping through an execution of the program, but they lack the ability to easily simulate failure scenarios and control the order in which messages are delivered. Oddity is a graphical, interactive debugger for distributed systems. It brings the power of traditional step-through debugging---fine-grained control and observation of a program as it executes---to distributed systems. It also enables exploratory testing, in which an engineer examines and perturbs the behavior of a system in order to better understand it, perhaps without a specific bug in mind. A programmer can directly control message and failure interleaving. Oddity supports time travel, allowing a developer to explore multiple branching executions of a system within a single debugging session. Above all, Oddity encourages distributed systems thinking: rather than assuming the normal case and attaching failure handling as an afterthought, distributed systems should be developed around the certainty of message loss and node failure. Graduate and undergraduate students used Oddity in two distributed systems classes. Usage tracking and qualitative surveys showed that students found Oddity useful for both debugging and exploratory testing.