In the late 1970s, using profits from their concert promotion Business, the brothers created a small independent film distribution company called Miramax, named after their parents – Miriam and Max. The company's first releases were primarily music-oriented concert films, such as Paul McCartney's Rockshow. In the early 1980s, Miramax acquired the rights to two British films of benefit shows filmed for the human rights organization Amnesty International. Working closely with Martin Lewis, the Producer of the original films, the Weinstein brothers edited the two films into one movie tailored for the American market. The resulting film, released as The Secret Policeman's Other Ball in May 1982, became Miramax's first hit. The movie raised considerable sums for Amnesty International and was credited by Amnesty with having helped to raise its profile in the US.

The Weinsteins slowly built upon this success throughout the 1980s with arthouse films that achieved critical attention and modest commercial success. Harvey Weinstein and Miramax gained wider attention in 1988 with the release of Errol Morris' documentary The Thin Blue Line, which detailed the struggle of Randall Adams, a wrongfully convicted inmate sentenced to death row. The publicity that soon surrounded the case resulted in Adams' release and nationwide publicity for Miramax. The following year, their successful launch release of Steven Soderbergh's Sex, Lies, and Videotape propelled Miramax to become the most successful independent studio in America.

Miramax continued to grow its library of films and Directors until, in 1993, Disney offered Harvey and Bob $80 million for ownership of Miramax. Agreeing to the deal that would cement their Hollywood clout and ensure that they would remain at the head of their company, Miramax followed the next year with their first blockbuster, Quentin Tarantino's Pulp Fiction.

1996 brought Miramax's first Academy Award for Best Picture with the victory of The English Patient. This would start a string of critical successes that would include Shakespeare in Love and Good Will Hunting.

Weinstein has been married twice. He has two daughters from his first marriage. Weinstein married Anne Clayton, a former book Editor, in 2000. They have three children and lived in a large townhouse on the Upper West Side. Anne filed for divorce in April 2012, and sought a protective order because she feared "bodily harm". Weinstein issued a statement from Don Sloane, a Washington-based interventionist who denied that Weinstein was a danger to his wife, and who said that Anne was reacting to a family intervention conducted to address her alcoholism. Anne's lawyers denied that their client suffered from any addiction, and said that Sloane's statement was from Weinstein's paid agent, who had never met Anne Weinstein.

On March 29, 2005, it was announced that the Weinstein brothers would leave Miramax on September 30 and would form their own production company, The Weinstein Company. Five years later, in 2010, Disney sold Miramax to the Qatari group Filmyard Holdings, who in turn sold it to the beIN Media Group in 2016.