Google has been dominating the search engine market for a while now; however, since Bing's launch back in 2009, Google has had to compete with an ever-growing rival creeping up on it. Microsoft's Bing has slowly been gaining market share, nibbling away at Google's domination piece-by-piece.
For April 2016 in the US, Bing grew by 0.2%, bringing it to 21.6% overall market share, whilst Google fell by 0.2%, coming down to 63.8% market share. Yahoo also saw an increase, albeit only by 0.1%, whereas Ask fell by 0.1% and AOL remained at its current share of 0.9%.
It is no surprise that Bing has been growing recently: Bing comes as the default search engine for Apple's Siri, as well as powering AOL's search functionality. The growth of Windows 10 may well have helped too, given that Bing is deeply integrated into the OS, via the taskbar search function and Cortana.
In 2012, Microsoft launched 'Bing it on', a challenge where users are asked to search for something, and are shown results side-by-side, from Google and Bing. Users are then asked to vote for each result, selecting the one which they find to be the best and most relevant. The company claimed that people preferred Bing "nearly 2-to-1 in blind comparison tests". You can try it out for yourself here.