Mr Jobs died in 2011 and was succeeded as chief executive by Tim Cook.
Part of the argument against a company hitting a trillion dollars in market value - and staying there - is finance's so-called law of large numbers. It now accounts for 4 percent of the S&P 500.
But a traditional industrial business, The Saudi Arabian Oil Company known as Aramco, could surpass Apple if it carries out plans to offer its stock to the public. However, it's not a bad thing, and puts down a marker for just how far the company has come.
The company's fortunes were turbocharged by the launch of personal gadgets such as the iPod in 2001 and the iPhone in 2007.
Market capitalization, or market cap, is the total combined value of all of a publicly traded company's outstanding shares.
In the more than four decades since Steve Jobs founded the company in a California garage, Apple has become almost synonymous with personal computing and mobile devices.
In 2006 the company had sales of less than $20bn and posted profits of nearly $2bn. Apple announced $100 billion in stock buybacks on May 1, the largest repurchase ever by a US public company. The company owes its success to a number of new and novel products that not only revolutionized the technology industry but, in many ways, changed the entire world.
Jeff Carbone, co-founder of Cornerstone Financial Partners in Charlotte, North Carolina, has included Apple in his clients' portfolios for about a decade.
China-based Huawei took the second-place spot from Apple in a tightening global smartphone market during the second quarter of this year, according to the International Data Corporation. "We're just waiting for tomorrow's payrolls", said Tom Simons, money market economist at Jefferies in NY.
The iPhone transformed Apple's fortunes.
Earlier today, the tech firm's own stock app jumped the gun and mistakenly said Apple had already broken this milestone.
The shares were soaring because of a better than expected set of results posted by Apple for the period between May and June.
Mr Jobs remained mercurial when he returned to Apple but he had also become more thoughtful and adept at spotting talent that would help him create a revolutionary innovation factory.