DNA single-strand breaks (SSBs) are the commonest DNA lesions arising spontaneously in cells, and if not repaired may block transcription or may be converted into potentially lethal/clastogenic DNA double-strand breaks (DSBs). Recently, evidence has emerged that defects in the rapid repair of SSBs preferentially impact the nervous system. In particular, spinocerebellar ataxia with axonal neuropathy (SCAN1) is a human disease that is associated with mutation of TDP1 (tyrosyl DNA phosphodiesterase 1) protein and with a defect in repairing certain types of SSBs. Although SCAN1 is a rare neurodegenerative disorder, understanding the molecular basis of this disease will lead to better understanding of neurodegenerative processes. Here we review recent progress in our understanding of TDP1, single-strand break repair (SSBR), and neurodegenerative disease.