Abrams was born in The Bronx, New York City, the son of Benjamin and Dorothy Abrams. He has one sister, Marlene (Abrams) Kitrosser. On September 15, 1974, he married the daughter of Jacob and Hilda Schulder, Diane Schulder Abrams, an attorney who created and taught the first "Women and the Law" course in an American law school. Diane has two siblings, Howard Schulder and Sylvia Schulder Fisher. Robert and Diane have two daughters, Rachel and Becky, and six grandchildren.
He graduated from Columbia College and the New York University School of Law. He is considered a member of the reform wing of the Democratic Party.
Abrams was a member of the New York State Assembly from 1966 to 1969, sitting in the 176th, 177th and 178th New York State Legislatures. From 1970 to 1978, he was Borough President of the Bronx and a member of the New York City Board of Estimate, having been elected in 1969 and overwhelmingly re-elected in 1973 and 1977.
He was a delegate to the 1972, 1976, 1980 and 1984 Democratic National Conventions. At the 1972 Democratic National Convention, he was the co-chair of the New York delegation and was at the microphone to cast New York's 272 votes for George McGovern. In 1980, he was the chairman of Senator Edward M. Kennedy's primary campaign for president in New York and led a strong victory over incumbent President Jimmy Carter. In 1988, he was a presidential elector, voting for Michael Dukakis- Lloyd Bentsen ticket.
Abrams was elected New York Attorney General in 1978, the first time in forty years a Democrat was elected to that post and was subsequently re-elected three times, in 1982, 1986, and 1990. He defeated future Republican Rep. Peter King in his 1986 re-election campaign for Attorney General. Abrams built a reputation as an activist and consumer advocate, taking on environmental polluters, charity frauds, discrimination in housing and various activities in the marketplace. He is also well known for the manner in which he sensitively and professionally handled an extremely difficult assignment, that of special prosecutor investigating the claims of Tawana Brawley. Governor Mario Cuomo directed him in 1988 to investigate the claims of Brawley, a black teen-ager, that she had been abducted and raped in upstate Dutchess County by a gang of whites. A lengthy grand jury inquiry supervised by Abrams' office later concluded that she had fabricated her story.
During his tenure as Attorney General, Abrams received numerous awards and honors and earned national prominence rarely achieved by a state-level official. He served as president of the National Association of Attorneys General and was selected by his colleagues to receive the coveted Wyman Award as Outstanding Attorney General in the Nation.
In 1992, he sought election to the United States Senate, to challenge Republican Senator Al D'Amato. He won the Democratic Primary, defeating former Congresswoman Geraldine Ferraro, Rev. Al Sharpton, and New York City Comptroller Elizabeth Holtzman. Abrams was initially the front-runner but by the end of the summer he was running second to Ferraro in polls. The nomination battle then took a bitter turn, particularly Holtzman and Abrams' attack on Ferraro's questionable business dealings which Ferraro interpreted as anti-Italian slurs. After Abrams emerged as the nominee, the Democrats remained divided and he was unable to secure Ferraro's endorsement until the last days of the campaign. Abrams was also criticized for calling D'Amato a Fascist, and he narrowly lost the general election as a result of these controversies.
After narrowly losing the Senate race, Abrams failed to realize his hopes for a cabinet post in the administration of President Bill Clinton. Abrams also wanted to run for Governor of New York, however fellow Democrat and incumbent Mario Cuomo decided to seek a fourth term. Despite making plans to run for re-election as state attorney general, Abrams announced his resignation from the office of attorney general on September 8, 1993, to take effect on December 31. He had a year left in his term.
Upon leaving government, Abrams joined Stroock & Stroock & Lavan as a partner. He has remained active in civic affairs in New York. In 1996, the New York University School of Law established an annual lecture program, the Attorney General Robert Abrams Public Service Lecture whereby each year a prominent public figure who has performed exemplary public service addresses the students, faculty and alumni of the law school to urge students to consider all or a portion of their career to be dedicated to public service.
Mayor Bloomberg appointed Abrams in 2005 to serve on the New York City Charter Revision Commission. In 2006, New York Governor Elect Eliot Spitzer appointed Abrams to serve as Co-Chair of his Policy Advisory Committee on Governmental Reform for his Transition, and New York Attorney General Elect Andrew Cuomo appointed him Executive Chair of his Transition Committee. In 2008, New York Governor David Paterson appointed Abrams to serve on the Board of the United Nations Development Corporation.
On May 9, 2009, New York Governor David Paterson renamed the Justice Building at the Empire State Plaza in Albany the Robert Abrams Building for Law and Justice. Also in 2009, Attorney General elect Eric Schneiderman appointed Abrams to serve as Honorary Co-Chair of his transition committee. In 2010, New York's Chief Judge Jonathan Lippman appointed him to be a member of the Advisory Council for the Retired Attorney Pro Bono Program.
In 2012, Governor Andrew Cuomo appointed Abrams as co-chairman of a Moreland Commission to investigate the preparedness and response of the utilities in New York State to Superstorm Sandy which took the lives of numerous New Yorkers and caused billions of dollars of damage. At the conclusion of its hearings and deliberations, the Commission released a report which resulted in changes to New York State law and practices by utilities.