In this review paper, low-speed computational work from NASA Langley Research Center in support of the Space Launch System (SLS) is discussed. This information includes both historical and present efforts with the Kestrel computational fluid dynamics solver. The low-speed aerodynamics of SLS is highly complex, and the analysis of the unsteady flowfield requires significant computational efforts. The SLS mission profile varies from the vehicle static on the launch pad through high-speed ascent. This study focuses on the prelaunch as well as liftoff and transition portions of the flight both in proximity to the launch tower and in isolation. High-alpha conditions, as large as 90 deg, result in a flowfield dominated by massive, large-scale flow separation and asymmetric vortices. High-fidelity solutions require an unsteady computational formulation to accurately capture the aerodynamics of the vehicle. A detailed discussion of the computational approach is presented, followed by key efforts to support the program, both historic and present, including information that has been either published previously or that has never before been published external to NASA.