Somatostatin (SST) is a well-known neuropeptide that is expressed throughout the brain. In the cortex, SST is expressed in a subset of GABAergic neurons and is known as a protein marker of inhibitory interneurons. Recent studies have identified the key functions of SST in modulating cortical circuits in the brain and cognitive function. Furthermore, reduced expression of SST is a hallmark of various neurological disorders, including Alzheimer's disease and depression. In this review, we summarize the current knowledge on SST expression and function in the brain. In particular, we describe the physiological roles of SST-positive interneurons in the cortex. We further describe the causal relationship between pathophysiological changes in SST function and various neurological disorders, such as Alzheimer's disease. Finally, we discuss potential treatments and possibility of novel drug developments for neurological disorders based on the current knowledge on the function of SST and SST analogs in the brain derived from experimental and clinical studies.