How to display blocks depending on the logged in user? How can I display blocks depending on the logged in user?

Let's say I have a Block1 and Block2. When user1 is logged in, that user should only see Block1, but user2 should only see Block2

I found the Logic Block module, but it doesn't seem to work for what I'm trying to do.
You could go to blocks setting and there are Roles tab.
If you check "anonymous user" - this block will visible only for not loggined user. If you check " authenticated user" - block will be visible loggined user.