To harness modern multicore processors, it is imperative to develop parallel versions of fundamental algorithms. In this paper, we present a general approach to best-first heuristic search in a shared-memory setting. Each thread attempts to expand the most promising nodes. By using abstraction to partition the state space, we detect duplicate states while avoiding lock contention. We allow speculative expansions when necessary to keep threads busy. We identify and fix po-tential livelock conditions. In an empirical comparison on STRIPS planning, grid pathfinding, and sliding tile puzzle problems using an 8-core machine, we show that A* imple-mented in our framework yields faster search performance than previous parallel search proposals. We also demonstrate that our approach extends easily to other best-first searches, such as weighted A* and anytime heuristic search.