The article presents a theoretical analysis of contemporary models of persistent stuttering development in children and adults at the current period of development of science. The accumulated amount of scientific knowledge suggests that stuttering has a neurological basis: it is associated with disorders in the structure and function of the brain. On this basis, there have been emerged models of stuttering that link the cause of a speech disorder with an unstable speech motor system. Theories and models of stuttering based on cognitive and language processing are likely to be useful in that they have explanatory power in relation to the mechanisms that play an important role in the production of key symptoms of stuttering. Considering that stuttering is a complex disorder, the logical result of this was the proposal of multifactorial models of impaired speech fluency. The presented overview may be useful to psychiatrists, clinical psychologists, speech therapists, teachers, and practitioners interacting with children and adults with stuttering and other speech fluency disorders.