 This paper proposes a set of backward reachability approaches for safety certification of neural feedback loops, NFLs. These approaches leverage existing forward NN analysis tools to calculate over, approximations to back projection, BP, sets, which are sets of states for which an NN policy will lead a system to a given target set. The authors demonstrate these methods on several examples, including a 6D model, showing their effectiveness in providing a computationally efficient way to certify safety of NFLs. This article was authored by Nicholas Rober, Sidney M. Katz, Chelsea Sidrain, and others.