Caching and persistence support efficient, convenient and transparent distributed data sharing. The most natural model of persistence is persistence by reachability, managed automatically by a garbage collector (GC). We propose a very general model of such a system (based on distributed shared memory) and a scalable, asynchronous distributed GC algorithm. Within this model, we show sufficient and widely applicable correctness conditions for the interactions between applications, store, memory, coherence, and GC. The GC runs as a set of processes (local to each participating machine) communicating by asynchronous messages. Collection does not interfere with applications by setting locks, polluting caches, or causing I/O; this requirement raised some novel and interesting challenges which we address in this article. The algorithm is safe and live; it is not complete, i.e. it collects some distributed cycles of garbage but not necessarily all.