For those of you that haven't heard yet, we have some great new features in SharePoint 2013 that enable hybrid environments between on-premises and o365 farms. These features allow you to use your BCS applications you have on premise in your o365 farm, and also to be able to see search results from one farm while in the other - i.e. if you are in your on-premise farm when you run a query you can see results from both your on-premise farm and o365 in one consolidated view. If you're lucky enough to be at the SharePoint Conference (SPC) this week you can see Brad Stevenson present on this topic with session SPC 243 - Hybrid Overview: Connecting SharePoint 2013 On-premises to SharePoint Online in Office365. Unfortunately I was going to be presenting this topic along with Brad but I got run over by one locomotive of a respiratory infection so I'm stuck just writing about it for now.
There's a lot of configuration and setup required to get this working, but we have a couple of resources to help you. First, we just published a set of whitepapers and documentation on getting this set up and going. You can visit the download center at http://technet.microsoft.com/en-us/library/jj838715.aspx to get an overview of the resources we have. If you follow the link on the bottom of the page to http://www.microsoft.com/en-us/download/details.aspx?id=35593 then you can download the papers. To set up a hybrid search environment you will want to download the sps-2013-config-one-way-hybrid-environment document or PDF.
If you are just interested in seeing a demo of how it works, here are some links to what Brad is going to show at SPC:
can we have a hybrid search with office 365 and SharePoint 2010 instance on premise?