unittest vs exceptions?

[Maxime Chevalier]

I'd like to write some unit tests to check my software. Writing 
unittest blocks and putting assert statements in there seems easy 
enough, but I noticed that if the code I run in there throws an 
exception, I don't get the unit test failed message.

How does unittest check for success/failure? Does assert throw a 
special kind of error class when it fails? How would you check 
that some code didn't throw an exception, or did throw an 
exception?