Rensselaer is a city in Rensselaer County, New York, United States, and is located on the east side of the Hudson River, opposite Albany and on the western border of Rensselaer County. As of the 2020 census, the city population was 9,210. The area now known as the City of Rensselaer was settled by the Dutch in the 17th century, who called it t'Greyn Bos, which became Greenbush in English.