Joan Rivers, a raucous and often-ubiquitous comedic presence on TV and nightclubs since the 1960s, has died. She was 81.

“It is with great sadness that I announce the death of my mother, Joan Rivers,” daughter Melissa Rivers, speaking for herself and her own son, Cooper, said in a statement obtained by PEOPLE.

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“She passed peacefully at 1:17 p.m. surrounded by family and close friends. My son and I would like to thank the doctors, nurses, and staff of Mount Sinai Hospital for the amazing care they provided for my mother. Cooper and I have found ourselves humbled by the outpouring of love, support, and prayers we have received from around the world. They have been heard and appreciated.

“My mother s greatest joy in life was to make people laugh. Although that is difficult to do right now, I know her final wish would be that we return to laughing soon.”

Rivers stopped breathing during a surgical procedure on her vocal cords last week and had to be rushed from the clinic to Mount Sinai Hospital.

Melissa Rivers immediately flew from Los Angeles to the Manhattan medical facility, where her mother reportedly had been placed in a medically induced coma.

In a statement over the weekend, Melissa Rivers said, “We are keeping our fingers crossed,” and thanked those who expressed their support as her mother fought for her life.

Smart, Driven – and Funny

Merciless with her material, shrewd with her tireless work ethic and highly successful in a world dominated by men, the Brooklyn-born Joan Alexandra Molinsky graduated Phi Beta Kappa from Barnard in 1954, then graduated to the Garment District of Manhattan, where she worked as the fashion coordinator for a clothing firm. It was there that she met and married the boss’s son, James Sanger, though the union only lasted six months.

Comedy beckoned – her agent, Tony Rivers suggested she change her name, so she took his – and her fierce desire to make it big, after years of struggling in comedy clubs and landing the occasional TV guest spot, caused her and her second husband and manager Edgar Rosenberg to mortgage their home so she could write and direct her first film, 1978’s Rabbit Test. It was about a man (a young Billy Crystal) who got pregnant. It flopped, but Rivers soldiered on.

It took late-night king Johnny Carson to make her – and then break her, but only for so long.

The Queen of Late Night

In 1965, the NBC Tonight Show host gave Rivers her first national exposure on the program, and by 1983 she was named permanent guest host whenever Carson took a night off, which was often. This was when her shtick grew increasingly outrageous, and the public would tune in just to hear her generally tasteless yet usually hilarious attacks on the high and the mighty.

Rivers held nothing and nobody sacred, be it the Queen of England (“If you own England, Ireland, Scotland and Canada – shave your legs!”), Elizabeth Taylor‘s increasingly expansive waistline (“She puts mayonnaise on aspirin”) or her own cosmetic surgical improvements (“I was the ugliest child ever born in Larchmont, New York. Oh, please! The doctor looked at me and slapped my mother”).

But when Rivers learned she was not in the running to replace Carson when he planned to retire, she accepted a $3 million offer and a three-year contract from Rupert Murdoch’s then-fledgling Fox network to host her own late-night program, to run opposite the Tonight Show.

Reportedly, when Rivers rang Carson to tell him the news, which he had already heard, he refused her call.

“I’m the only woman in the history of the world who left Johnny Carson and didn’t ask him for money,” Rivers quipped about the much-married TV star. As for her relationship with NBC, she remained banished from Tonight all through the Jay Leno era, until Jimmy Fallon would invite her back in March 2014, after an absence of 26 years.

The Fox show did not succeed, and its failure, as well as Rosenberg’s recent heart attack, plunged Rivers’s husband into a depression so deep that, in 1987, Rosenberg committed suicide. He and Rivers had been married 22 years, and her life, she later admitted, went into a tailspin. Her showbiz contracts dried up, because suicide just wasn’t funny. She became bulimic. And she and Edgar’s only child, Melissa Rivers, who was born in 1968, stopped speaking.

Career Revival

In time, mother and daughter patched up their relationship, and Rivers revived her career, which also included the development of product lines for QVC. Playing themselves, they starred together in the 1994 TV docudrama Tears and Laughter: The Joan and Melissa Rivers Story, then began a prolific – and profitable – association with the E! cable network, where they rubbed shoulders with the stars and then, behinds their backs, dished on what they were wearing.

At the time of her death, Rivers, who is survived by her daughter and a grandson, Edgar Cooper Endicott (born in 2000), was the highly popular star of E!’s Fashion Police and the host of the online talk show In Bed with Joan. She and Melissa also costarred on the WEtv reality show Joan & Melissa: Joan Knows Best?

Rivers, whose tragic death closely follows the shocking loss of another comedy legend, Robin Williams, once said that when it came to her craft, “Humor doesn’t come out of the good times, it comes out of the anger, pain and sorrow. Always the anger.”

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