With the gifts open and the fun well under way, retailers around the globe are turning to their books to see just how successful the 2016 holiday season was. For Amazon, it's smiles all around as the e-commerce giant turned in a stellar performance leading up to Christmas.

Amazon said on Tuesday that it shipped more than a billion items worldwide during the holiday season with some of its best-sellers being Amazon's own devices like the Echo and Echo Dot. Indeed, an Echo Dot was given as a gift at multiple events I attended over the past several days.

Jeff Wilke, CEO Worldwide Consumer, Amazon, said that despite their best efforts and ramped-up production, they still had trouble keeping Echo and Echo Dot in stock.

December 19 marked the company's peak worldwide shipping day this holiday season.

Unsurprisingly, Amazon notes that nearly three out of four customers (72 percent, to be exact) shopped for the holidays using a mobile device. On Cyber Monday alone, customers on mobile devices purchases around 46 electronics per second and 36 toys per second.

Amazon was also instrumental in helping make the holidays special for others as it employed more than 200,000 full-time and seasonal associates to help with the influx of orders. This is in addition to the more than 45,000 robotics units it had working alongside humans in some 20+ fulfillment centers.