Krylov methods are the most effective synchronous linear solvers, but the inner products require synchronization so pose a challenge for asynchronous solvers. Preconditioning can still be useful for other related methods, such as Richardson iteration. We discuss asynchronous preconditioning with emphasis on incomplete factorizations. We show that ATS-ILU, a new iterative ILU method that has both a synchronous and asynchronous version, is highly competitive with the well known ParILU method.