The Dow closed above 36,000 for the first time. The S&P 500 jumped 16 points. The Nasdaq rallied 53.

Investors expect to hear at the end of the Fed's Wednesday meeting how it will wind-down its massive bond-buying program and when the rate hikes might begin.

DataTrek Research Co-founder Nick Colas:

"And then the market is going to give, I think the Fed some leeway to say either: 'We'll see how things are, you know, in the first quarter, second quarter of next year and go,' or if the Fed wants to say, 'Look, we understand inflation is a concern and we hear you,' the market also accepts that as a good outcome. And either way, I think the market is giving the Fed a lot of benefit of the doubt to address the inflation issue without tanking the economy in the back half of next year."

Meanwhile, earnings season continues to boost stock prices.

Under Armour raised its revenue and profit forecasts for the year after a strong quarter. The athletic gear maker said supply chain disruptions that snarled the apparel industry are starting to ease. The stock soared roughly 16-1/2 percent.

Pfizer raised its full-year sales forecast on the strength of its vaccine business. The stock was up more than 4 percent.

But the stock of the day: Avis Budget. The meme-stock phenomenon returned in full force after the car rental company topped quarterly forecasts - by far. The stock doubled as retail investors put the squeeze on professional investors who were betting the stock would fall.

Sticking with rental cars, Elon Musk set-off confusion with a tweet saying a deal has not been signed for Tesla to sell 100,000 electric cars to Hertz. Hertz fired back and defended the announcement it made last week, by saying it has already started receiving Tesla cars. Shares of Tesla fell on the day.