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This paper considers the callback reachability problem --- determining if a callback can be called by an event-driven framework in an unexpected state. Event-driven programming frameworks are pervasive for creating user-interactive applications (apps) on just about every modern platform. Control flow between callbacks is determined by the framework and largely opaque to the programmer. This opacity of the callback control flow not only causes difficulty for the programmer but is also difficult for those developing static analysis. Previous static analysis techniques address this opacity either by assuming an arbitrary framework implementation or attempting to eagerly specify all possible callback control flow, but this is either too coarse to prove properties requiring callback-ordering constraints or too burdensome and tricky to get right. Instead, we present a middle way where the callback control flow can be gradually refined in a targeted manner to prove assertions of interest. The key insight to get this middle way is by reasoning about the history of method invocations at the boundary between app and framework code --- enabling a decoupling of the specification of callback control flow from the analysis of app code. We call the sequence of such boundary-method invocations message histories and develop message-history logics to do this reasoning. In particular, we define the notion of an application-only transition system with boundary transitions, a message-history program logic for programs with such transitions, and a temporal specification logic for capturing callback control flow in a targeted and compositional manner. Then to utilize the logics in a goal-directed verifier, we define a way to combine after-the-fact an assertion about message histories with a specification of callback control flow. We implemented a prototype message history-based verifier called Historia and provide evidence that our approach is uniquely capable of distinguishing between buggy and fixed versions on challenging examples drawn from real-world issues and that our targeted specification approach enables proving the absence of multi-callback bug patterns in real-world open-source Android apps.