Creativity, meant as the ability to produce novel, original and suitable ideas, has received increased attention by research in the last years, especially from neuroaesthetics and social neuroscience. Besides the research conducted on the neural correlates of such capacities, previous work tried to answer the question of whether it is possible to enhance creativity through cognitive and neural stimulation. In particular, transcranial direct current stimulation (tDCS) has been applied to increase neuronal excitability in those areas related to creativity. However, being a complex construct that applies to a huge variety of situations, available results are often confusing and inconsistent. Thus, in the present critical review, after selecting original research articles investigating creativity with tDCS, results will be reviewed and framed according to the different effects of tDCS and its underlying mechanisms, which can be defined as follows: the promotion of self-focused attention; the disruption of inhibiting mechanisms; the enhancement of creative thinking; the promotion of artistic enactment. Finally, a theoretical perspective, the creative on/off model, will be provided to integrate the reported evidence with respect to both anatomical and functional issues and propose a cognitive explanation of the emergence of creative thinking.