Drug misuse is a significant social and public health problem worldwide. Misused substances exert their neurobehavioural effects through changing neural signalling within the brain, many of them leading to substance dependence and addiction in the longer term. Among drugs with addictive liability, there are illicit classical stimulants such as cocaine and amphetamine, and their more recently available counterparts known as novel psychoactive substances (NPS). Stimulants normally increase dopamine availability in the brain, including the pathway implicated in reward-related behaviour. This pattern is observed in both animal and human brain. The main biological target of stimulants, both classical and NPS, is the dopamine transporter (DAT) implicated in the dopamine-enhancing effects of these drugs. This article aims at reviewing research on the molecular mechanisms underpinning the interactions between stimulant NPS, such as benzofurans, cathinones or piperidine derivatives and DAT, to achieve a greater understanding of the core phenomena that decide about the addictive potential of stimulant NPS. As the methodology is essential in the process of experimental research in this area, we review the applications of in vitro, in vivo and in silico approaches. The latter, including molecular dynamics, attracts the focus of the present review as the method of choice in molecular and atomistic investigations of the mechanisms of addiction of stimulant NPS. Research of this kind is of interest to not only scientists but also health professionals as updated knowledge of NPS, their modes of action and health risks, is needed to tackle the challenges posed by NPS misuse.