7.3.2 is the latest version. You'll need to ask your support organisation for a copy of the software and a new license key to replace the one to have. On the documentation CD there is a complete upgrade guide with all the steps. To get the best out of an upgrade, you might want to consider using the same people who did your origonal installation and learn by working with them or get the whole process documented for your site. This is an enterprise product and to get the best out of it needs a bit of experience and tweaking.
I took our enviroment from 7.2.6 to 7.3.2 without any problems. I've only seen positives so far. As Dave mentioned, you'll need to read the documentation as there are some steps that need to be done to bring parts of the database inline with the current version.
I upgraded from 7.2.4. Had to do some significant work in preparation. Make sure you UAT and test it properly before doing it for real on your live application. But very worth while though.
Thanks everyone for your posts. I felt like I was flying blind. Now, I have some direction.