People spend a remarkable 30-50% of awake life thinking about something other than what they are currently doing. These experiences of being "off-task" can be described as spontaneous thought when mental dynamics are relatively flexible. Here we review recent neuroscience developments in this area and consider implications for mental wellbeing and illness. We provide updated overviews of the roles of the default mode network and large-scale network dynamics, and we discuss emerging candidate mechanisms involving hippocampal memory (sharp-wave ripples, replay) and neuromodulatory (noradrenergic and serotonergic) systems. We explore how distinct brain states can be associated with or give rise to adaptive and maladaptive forms of thought linked to distinguishable mental health outcomes. We conclude by outlining new directions in the neuroscience of spontaneous and off-task thought that may clarify mechanisms, lead to personalized biomarkers, and facilitate therapy developments toward the goals of better understanding and improving mental health.