Here is a quick rundown of the areas that will be affected if a user is blocked:
Public Rooms - A blocked user will not be able to enter a public room that you own. However, they can still enter any room you are in at the moment, provided it is not yours.
IMVU Marriage - Your IMVU marriage will be automatically terminated once you block your partner.
Group Invites - A person who has been blocked will no longer be able to send a group invite to the person who blocked him.
Badge Granting - A person who has been blocked can no longer send a badge to the person who blocked him.
Credit Gifting - A person who has been blocked can no longer send credits to the person who blocked him.
Chat Invites - A person who has been blocked can no longer send chat invites to the person who blocked him. Further more, the blocker will not receive any "Missed Chat Invite" notification from the blocked person.
Product Reviews - A person who was blocked can still purchase the items of the person who blocked him (if the blocker is a Creator), but the blocked user can no longer leave any reviews on the blocker's product.
Feed Comments - As of the moment, blocked users can still reply to your Feed comments. This is a bug we are working on fixing.
Search - Blocked users cannot search for your avatar. However, they might be able to see that you blocked them when they look up the users in a room where you are in.
As you have seen, blocking is a very powerful tool that can be used to stop a harasser avatar from following you through different means. In order to learn more about blocking, you may watch check out this article. Also, you may unblock a user at any time you wish, as well as manage other aspects of your blocklist using this tool.
