Joan Rivers, a talk-show host, actress and red-carpet critic who rose to the top of comedy's ranks while unapologetically skewering everyone and everything she passed along the way, died Thursday in New York following complications from a medical procedure. She was 81 years old.

"She passed peacefully at 1:17 p.m. surrounded by family and close friends," her daughter, Melissa Rivers, said in a statement.

One...