Mitochondrial diseases are a large class of human hereditary diseases, accompanied by the dysfunction of mitochondria and the disruption of cellular energy synthesis, that affect various tissues and organ systems. Mitochondrial DNA mutation-caused disorders are difficult to study because of the insufficient number of clinical cases and the challenges of creating appropriate models. There are many cellular models of mitochondrial diseases, but their application has a number of limitations. The most proper and promising models of mitochondrial diseases are animal models, which, unfortunately, are quite rare and more difficult to develop. The challenges mainly arise from the structural features of mitochondria, which complicate the genetic editing of mitochondrial DNA. This review is devoted to discussing animal models of human mitochondrial diseases and recently developed approaches used to create them. Furthermore, this review discusses mitochondrial diseases and studies of metabolic disorders caused by the mitochondrial DNA mutations underlying these diseases.