The measurement of Pavlovian forms of fear extinction offers a relatively simple behavioral preparation that is nonetheless tractable, from a translational perspective, as an approach to study mechanisms of exposure therapy and biological underpinnings of anxiety and trauma-related disorders such as post-traumatic stress disorder (PTSD). Deficient fear extinction is considered a robust clinical endophenotype for these disorders and, as such, has particular significance in the current “age of RDoC (research domain criteria).” Various rodent models of impaired extinction have thus been generated with the objective of approximating this clinical, relapse prone aberrant extinction learning. These models have helped to reveal neurobiological correlates of extinction circuitry failure, gene variants, and other mechanisms underlying deficient fear extinction. In addition, they are increasingly serving as tools to investigate ways to therapeutically overcome poor extinction to support long-term retention of extinction memory and thus protection against various forms of fear relapse; modeled in the laboratory by measuring spontaneous recovery, reinstatement and renewal of fear. In the current article, we review models of impaired extinction built around (1) experimentally induced brain region and neural circuit disruptions (2) spontaneously-arising and laboratory-induced genetic modifications, or (3) exposure to environmental insults, including stress, drugs of abuse, and unhealthy diet. Collectively, these models have been instrumental in advancing in our understanding of extinction failure and underlying susceptibilities at the neural, genetic, molecular, and neurochemical levels; generating renewed interest in developing novel, targeted and effective therapeutic treatments for anxiety and trauma-related disorders.