This review surveys the dramatic variations in wake structures and flow transitions, in addition to body forces, that appear as the motion of bluff bodies through a fluid occurs increasingly closer to a solid wall. In particular, we discuss the two cases of bluff bodies translating parallel to solid walls at varying heights and bluff bodies impacting on solid walls. In the former case, we highlight the changes to the wake structures as the flow varies from that of an isolated body to that of a body on or very close to the wall, including the effects when the body is rotating. For the latter case of an impacting body, we review the flow structures following impact and their transition to three-dimensionality. We discuss the issue of whether there is solid–solid contact between the bluff body and a wall and its importance to body motion. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 53 is January 6, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.