This research study will examine if a targeted computerized cognitive remediation (CCR) training program is better for treating geriatric depression than general computer activity. We will also examine whether this intervention is related to improvement in cognitive and depressive symptoms. Elderly patients with depression, who have, and who have not been treated with antidepressant medication for their illness, will be recruited to participate in either a 30 hour cognitive remediation program or general computer activity designed to be both challenging and interesting. They will be asked to complete between 1 and 3 hours of remediation per day over 4 weeks. While undergoing the cognitive remediation participants will be asked questions to assess their symptoms of, as well as the severity of, their depression weekly. This will inform researchers about whether or not the CCR is helping to improve depressive symptoms. At the end of the CCR study, participants will be given a battery of cognitive tests design to tell investigators whether or not the CCR improved their thinking in a variety of different ways including improving attention, memory, and organization. Investigators will also determine whether changes in participants' thinking are related to changes in their mood or other depressive symptoms. It is hoped that information gained from this study will help investigators to better understand the brain processes associated with depression, recovery from depression, and will help inform the development of future alternative treatments for this illness.