Hoarding disorder (HD) is associated with significant personal impairment in function and constitutes a severe public health burden. Individuals who hoard experience intense distress in discarding a large number of objects, which results in extreme clutter. Research and theory suggest that hoarding may be associated with specific deficits in information processing, particularly in the areas of attention, memory, and executive functioning. There is also growing interest in the neural underpinnings of hoarding behavior. Thus, the primary aim of this review is to summarize the current state of evidence regarding neuropsychological deficits associated with hoarding and review research on its neurophysiological underpinnings. We also outline the prominent theoretical model of hoarding and provide an up-to-date description of empirically based psychological and medical treatment approaches for HD. Finally, we discuss important future avenues for elaborating our model of HD and improving treatment access and outcomes for this disabling disorder.