Despite a contentious relationship, Google recently received their Internet Content Provider permit from the Chinese government. Google wouldn't comment beyond confirming that the license has been renewed in China, a search market Baidu dominates.
Google's History with China
Google launched their Chinese site back in 2005, but things didn't stay smooth for long. In addition to self-censorship requirements from the Chinese government (which required Google to block gambling sites, pornography, and any content deemed critical of the communist government), China moved to block access to YouTube in 2009.
Then, in early 2010, Google announced that the user accounts of humanitarian activists and others had been hacked, implying without stating outright that the origin of the attack was the Chinese government. Google then announced they would be leaving the Chinese market in response to both the hacking attempts and the censorship. They instead re-directed users to the Hong Kong version of Google, which was uncensored.
It's been suspected for a while, however, that Google wants to return. In January of this year, Eric Schmidt stated that he wanted the company to return to China – "appropriately and within our policies." He argued that as a company whose objective is to organize the world's information, ignoring a billion people just wouldn't work.
Google's Future in China?
Google comes in as a distant second to Baidu, China's leading search engine. However, targeted marketing, optimized local results, and maybe even lower censorship could draw users to the Google empire.
But will that happen? Google certainly left in a storm, but they have now renewed their permit for operating an Internet-based company in China. That could simply be meant to cover other technologies, such as Maps, Google+ or Gmail, but it opens the door for search.