Weak memory models formalize the inconsistent behaviors that one can expect to observe in multithreaded programs running on modern hardware. In so doing, however, they complicate the already-difficult task of reasoning about correctness of concurrent code. Worse, they render impotent the sophisticated formal methods that have been developed to tame concurrency, which almost universally assume a strong (i.e. sequentially consistent) memory model. This paper introduces GPS, the first program logic to provide a full-fledged suite of modern verification techniques---including ghost state, protocols, and separation logic---for high-level, structured reasoning about weak memory. We demonstrate the effectiveness of GPS by applying it to challenging examples drawn from the Linux kernel as well as lock-free data structures. We also define the semantics of GPS and prove in Coq that it is sound with respect to the axiomatic C11 weak memory model.