Dealing with open boundaries in the computer simulation of unsteady subsonic shear flows presents challenging problems. In practice, only a portion of the flow can be investigated and we must ensure that the presence of artificial boundaries does not pollute the solution in a significant way. One difficulty is related to the basic solution of the physical flow equations and involves choosing appropriate nonlocal open boundary conditions at the outflow boundaries which will adequately bound the computational domain while providing information about the virtual flow behavior outside. A second difficulty is related to the discretized computational problem, for which additional numerical boundary conditions that are consistent with the unsteady flow equations at the boundaries are required for closure. Recent approaches based on characteristic analysis and their practical implementation are discussed. Specific examples are used to illustrate the implementation of state-of-the-art approaches to open boundary conditions and, in particular, the potential sensitivity of subsonic free shear flows to the actual choice of open boundary conditions. This sensitivity is an intrinsic feature of the flows being studied rather than an artifact of the computations. Ideal free shear flows do not exist; actual flow realizations are defined by the numerical or laboratory boundary conditions in the experiments. 1994 Academic Press, Inc.