Anyone upgraded from Sharepoint 2010 to 2013? I've heard that you can do the upgrade and then upgrade sites as and when you like and until then they effectively carry on using Sharepoint 2010. Any one found any issues with this?

We have a reporting system that uses Sharepoint that was created by another school. They have said it all should work but I am hesitant to upgrade it until I know for sure. We were going to create a test lab, upgrade and check but the issue is that we now need to upgrade to 2013 for our Parent external access so it is a bit time critical now. Would like some kind reassuring words!