Neurodegenerative diseases and depression are multifactorial disorders with a complex and poorly understood physiopathology. Astrocytes play a key role in the functioning of neurons in norm and pathology. Stress is an important factor for the development of brain disorders. Here, we review data on the effects of stress on astrocyte function and evidence of the involvement of astrocyte dysfunction in depression and Alzheimer’s disease (AD). Stressful life events are an important risk factor for depression; meanwhile, depression is an important risk factor for AD. Clinical data indicate atrophic changes in the same areas of the brain, the hippocampus and prefrontal cortex (PFC), in both pathologies. These brain regions play a key role in regulating the stress response and are most vulnerable to the action of glucocorticoids. PFC astrocytes are critically involved in the development of depression. Stress alters astrocyte function and can result in pyroptotic death of not only neurons, but also astrocytes. BDNF-TrkB system not only plays a key role in depression and in normalizing the stress response, but also appears to be an important factor in the functioning of astrocytes. Astrocytes, being a target for stress and glucocorticoids, are a promising target for the treatment of stress-dependent depression and AD.