Summer, who is best known for her 1970s hits 'I Feel Love' and 'Love to Love You Baby', passed away yesterday in Florida. It is thought that she lost her battle with lung cancer.
US President Barack Obama said "Her voice was unforgettable...The music industry has lost a legend far too soon."
Singer Barbra Streisand, who duetted with Summer on the 1979 hit No More Tears (Enough Is Enough), said she was "shocked" to hear of her passing.
Many fans have flocked to her star on the walk of fame in Hollywood, and other celebrities such as Elton John, Dolly Parton and Kylie Minogue have expressed their sadness through Twitter.
In a statement released on Thursday, her family said they were "at peace celebrating her extraordinary life and her continued legacy".
She had worked with producers Giorgio Moroder and Pete Bellotte in the 1970s as her career began to take off.
Moroder told BBC 5 Live she would be remembered "for her incredible voice and talent" and that her song I Feel Love "was really the start of electronic dance".
Summer had been living in Naples, Florida with her husband Bruce Sudano. She is survived by their daughters Brooklyn and Amanda and by Mimi, her daughter from her first marriage.