Impaired healing wounds do not proceed through the normal healing processes in a timely and orderly manner, and while they do eventually heal, their healing is not optimal. Chronic wounds, on the other hand, remain unhealed for weeks or months. In the US alone, chronic wounds impact ~8.5 million people and cost ~USD 28–90 billion per year, not accounting for the psychological and physical pain and emotional suffering that patients endure. These numbers are only expected to rise in the future as the elderly populations and the incidence of comorbidities such as diabetes, hypertension, and obesity increase. Over the last few decades, scientists have used a variety of approaches to treat chronic wounds, but unfortunately, to date, there is no effective treatment. Indeed, while there are thousands of drugs to combat cancer, there is only one single drug approved for the treatment of chronic wounds. This is in part because wound healing is a very complex process involving many phases that must occur sequentially and in a timely manner. Furthermore, models that fully mimic human chronic wounds have not been developed. In this review, we assess various models currently being used to study the biology of impaired healing and chronic non-healing wounds. Among them, this paper also highlights one model which shows significant promise; this model uses aged and obese db/db−/− mice and the chronic wounds that develop show characteristics of human chronic wounds that include increased oxidative stress, chronic inflammation, damaged microvasculature, abnormal collagen matrix deposition, a lack of re-epithelialization, and the spontaneous development of multi-bacterial biofilm. We also discuss how important it is that we continue to develop chronic wound models that more closely mimic those of humans and that can be used to test potential treatments to heal chronic wounds.