Google and Twitter have struck a deal that will lead to the search engine monolith once again indexing Tweets in real time. No one knows if indexed Tweets will come up in a Realtime type environment (You might remember several years ago the Realtime results in Google, which included Tweets, among other newsy-type results. It disappeared in early July 2011) or just under the "News" category in Google search. It's important to see this information as it's produced, because it's very timely and focused.
Tweets have been indexed since the death of Realtime in 2011, but they are hard to come by- mostly only very trending topics posted by people with over a million followers. Obviously not the majority.
As of today, I am not seeing Tweets in the SERPs for some top-trending topics, such as the Saturday Night Live 40th anniversary or the massive snow storms on the east coast. According to one article, the Twitter indexing will happen in the "first half" of 2015, so that means any time between now and June.
What this means for businesses is that if you aren't Tweeting, you should be, and if you are Tweeting, you should be more careful about it. When you Tweet, make sure you are spelling everything correctly and using good syntax. You can really make a mess in 140 characters. You MUST be careful. There are stories of people's lives/careers/businesses being ruined by poorly calculated "jokes" on Twitter. Keep it positive and stay away from politics/religion/touchy subjects. This is not to say that you shouldn't tweet scripture verses if you bill yourself as a faith-based business, but don't go on a rampage about "those" people, whoever they might be. The best advice I have is to use common sense. If it seems too close to the edge, it probably is.
Let me know if you start to see Twitter results in Google!
Local, Social Media and Education Support