Steve Jobs, co-founder and former chief executive of US technology giant Apple, has died at the age of 56.
Apple said he had been "the source of countless innovations that enrich and improve all of our lives" and had made the world "immeasurably better".
Mr Jobs had announced he was suffering from pancreatic cancer in 2004.
Tributes have been made by technology company bosses and world leaders, with US President Barack Obama saying the world had "lost a visionary".
"Steve was among the greatest of American innovators - brave enough to think differently, bold enough to believe he could change the world, and talented enough to do it," said Mr Obama.
A statement from Mr Jobs's family said they were with him when he died peacefully on Wednesday.
"In his public life, Steve was known as a visionary; in his private life, he cherished his family," they said, requesting privacy and thanking those who had "shared their wishes and prayers" during his final year.
Apple said the company had "lost a visionary and creative genius, and the world has lost an amazing human being".
Tim Cook, who was made Apple's CEO after Mr Jobs stood down in August, said his predecessor had left behind "a company that only he could have built, and his spirit will forever be the foundation of Apple".
Flags are being flown at half mast outside the Apple headquarters in Cupertino, California, while fans of the company have left tributes outside Apple shops around the world.
"What he's done for us as a culture, it resonates uniquely in every person," said Cory Moll, an Apple employee in San Francisco.
"Even if they never use an Apple product, the impact they have had is so far-reaching."
At the company's Shanghai shop, customer Jin Yi said Mr Jobs had created gadgets which had "changed people's perceptions of machines".
The heads of other leading technology companies have also paid tribute, including Microsoft boss Bill Gates, who said Mr Jobs's "profound impact" on the world of technology would "be felt for many generations to come".
"For those of us lucky enough to get to work with him, it's been an insanely great honour. I will miss Steve immensely."
Facebook founder Mark Zuckerberg thanks Mr Jobs for "showing that what you build can change the world" while Sony Corp president and CEO Howard Stringer said: "The digital age has lost its leading light."
South Korea's Samsung, which is involved in an ongoing legal battle with Apple over patents, praised Mr Jobs for his "numerous revolutionary changes to the information technology industry".
"His innovative spirit and remarkable accomplishments will forever be remembered by people around the world," said chief executive officer Choi Gee-Sung.
Mr Jobs built a reputation as a forthright and demanding leader who could take niche technologies - such as the mouse and graphical user interface, using onscreen icons rather than text - and make them popular with the general public.
He introduced the colourful iMac computer, the iPod, the iPhone and the iPad to the world. His death came just a day after Apple unveiled its latest iPhone 4S model.
With a market value estimated at $351bn (£227bn), Apple became the world's most valuable technology company.
'Face of Apple'
More than almost any other business leader, Mr Jobs was indistinguishable from his company, which he co-founded in the 1970s.
As the face of Apple, he represented its dedication to high-end technology and fashionable design.
And inside the company he exerted a level of influence unheard of in most businesses.
In 2004, Mr Jobs announced that he was suffering from pancreatic cancer. He had a liver transplant five years later.
In January, he took medical leave, before resigning as CEO in August and handing over his duties to Mr Cook.
In his resignation letter, Mr Jobs said: "I believe Apple's brightest and most innovative days are ahead of it. And I look forward to watching and contributing to its success in a new role."
However, Mr Jobs stayed on as Apple's chairman.
Despite his high profile, he remained fiercely protective of his private life.
He married his wife Laurene in 1991, and the couple had three children.
Mr Jobs also leaves a daughter from a previous relationship, and as an adult he discovered that he had a biological sister, US novelist Mona Simpson.