Stephen van Rensselaer established the Rensselaer School on November 5, 1824 with a letter to the Rev. Dr. Samuel Blatchford, in which Van Rensselaer asked Blatchford to serve as the first president. Within the letter he set down several orders of business. He appointed Amos Eaton as the school's first senior professor and appointed the first board of trustees. The school opened on Monday, January 3, 1825 at the Old Bank Place, a building at the north end of Troy. Tuition was around $40 per semester (equivalent to $800 in 2012). The fact that the school attracted students from as far as Ohio and Pennsylvania is attributed to the reputation of Eaton. Fourteen months of successful trial led to the incorporation of the school on March 21, 1826 by the state of New York. In its early years, the Rensselaer School strongly resembled a graduate school more than it did a college, drawing graduates from many older institutions.
Under Eaton, the Rensselaer School, renamed the Rensselaer Institute in 1832, was a small but vibrant center for technological research. The first civil engineering degrees in the United States were granted by the school in 1835, and many of the best remembered civil engineers of that time graduated from the school. Important visiting scholars included Joseph Henry, who had previously studied under Amos Eaton, and Thomas Davenport, who sold the world's first working electric motor to the institute.
In 1847 alumnus Benjamin Franklin Greene became the new senior professor. Earlier he had done a thorough study of European technical schools to see how Rensselaer could be improved. In 1850 he reorganized the school into a three-year polytechnic institute with six technical schools.In 1861 the name was changed to Rensselaer Polytechnic Institute. A severe conflagration of May 10, 1862, known as "The Great Fire", destroyed more than 507 buildings in Troy and gutted 75 acres (300,000 m2) in the heart of the city. The "Infant School" building that housed the Institute at the time was destroyed in this fire. Columbia University proposed that Rensselaer leave Troy altogether and merge with its New York City campus. Ultimately, the proposal was rejected and the campus left the crowded downtown for the hillside. Classes were temporarily held at the Vail House and in the Troy University building until 1864, when the Institute moved to a building on Broadway on 8th Street, now the site of the Approach.
One of the first Latino student organizations in the United States was founded at RPI in 1890. The Club Hispano Americano was established by the international Latin American students that attended the institute at this time.
In 1904 the Institute was for the fourth time devastated by fire, when its main building was completely destroyed. However, RPI underwent a period of academic and resource expansion under the leadership of President Palmer Ricketts. Named President in 1901, Ricketts liberalized the curriculum by adding the Department of Arts, Science, and Business Administration, in addition to the Graduate School. He also expanded the university's resources and developed RPI into a true polytechnic institute by increasing the number of degrees offered from two to twelve; these included electrical engineering, mechanical engineering, biology, chemistry, and physics. During Rickett's tenure, enrollment increased from approximately 200 in 1900 to a high of 1,700 in 1930.
Another period of expansion occurred following World War II as returning veterans used their GI Bill education benefits to attend college. The "Freshman Hill" residence complex was opened in 1953 followed by the completion of the Commons Dining Hall in 1954, two more halls in 1958, and three more in 1968. In 1961 there was major progress in academics at the institute with the construction of the Gaerttner Linear Accelerator, then the most powerful in the world, and the Jonsson-Rowland Science Center. The current Student Union building was opened in 1967.
The next three decades brought continued growth with many new buildings (see 'Campus' below), and growing ties to industry. The "H-building", previously used for storage, became the home for the RPI incubator program, the first such program sponsored solely by a university. Shortly after this, RPI decided to invest $3 million in pavement, water and power on around 1,200 acres (490 ha) of land it owned 5 miles (8.0 km) south of campus to create the Rensselaer Technology Park. In 1982 the New York State legislature granted RPI $30 million to build the George M. Low Center for Industrial Innovation, a center for industry-sponsored research and development.
In 1999, RPI gained attention when it was one of the first universities to implement a mandatory laptop computer program. This was also the year of the arrival of President Shirley Ann Jackson, a former chairperson of the Nuclear Regulatory Commission. She instituted the "The Rensselaer Plan" (discussed below), an ambitious plan to revitalize the institute. Many advances have been made under the plan, and Jackson has enjoyed the ongoing support of the RPI Board of Trustees. However, her leadership style did not sit well with many faculty; on April 26, 2006, RPI faculty voted 149 to 155 in a failed vote of no-confidence in Jackson. In September 2007, RPI's Faculty Senate was suspended for over four years over conflict with the administration. On October 4, 2008, RPI celebrated the opening of the $220 million Experimental Media and Performing Arts Center. That same year the national economic downturn resulted in the elimination of 98 staff positions across the Institute, about five percent of the workforce. Campus construction expansion continued, however, with the completion of the $92 million East Campus Athletic Village and opening of the new Blitman Commons residence hall in 2009. As of 2015, all staff positions had been reinstated at the Institute, experiencing significant growth from pre-recession levels and contributing over $1 billion annually to the economy of the Capital District. That same year, renovation of the North Hall, E-Complex, and Quadrangle dormitories began and was later completed in 2016 to house the largest incoming class in Rensselaer's history.