One contribution of 13 to a theme issue 'New frontiers for statistical learning in the cognitive sciences'. The cerebellum has been shown to be important for skill learning, including the learning of motor sequences. We investigated whether cerebellar transcranial direct current stimulation (tDCS) would enhance learning of fine motor sequences. Because the ability to generalize or transfer to novel task variations or circumstances is a crucial goal of real world training, we also examined the effect of tDCS on performance of novel sequences after training. In Study 1, participants received either anodal, cathodal or sham stimulation while simultaneously practising three eight-element key press sequences in a non-repeating, interleaved order. Immediately after sequence practice with concurrent tDCS, a transfer session was given in which participants practised three interleaved novel sequences. No stimulation was given during transfer. An inhibitory effect of cathodal tDCS was found during practice, such that the rate of learning was slowed in comparison to the anodal and sham groups. In Study 2, participants received anodal or sham stimulation and a 24 h delay was added between the practice and transfer sessions to reduce mental fatigue. Although this consolidation period benefitted subsequent transfer for both tDCS groups, anodal tDCS enhanced transfer performance.Together, these studies demonstrate polarity-specific effects on fine motor sequence learning and generalization.This article is part of the themed issue 'New frontiers for statistical learning in the cognitive sciences'.