(Is there a link that should be here, but isn't? Let me know!)
Block B's official Twitter feed is here, its Daum fan cafe site is here, its Instagram is here, and its Facebook page is here. Seven Seasons/KQ Entertainment, Block B's management company, has a Facebook page, a Web site, a You Tube channel, and a Twitter feed. Block B also has a Weibo account (Chinese/中文), a Japanese (日本語) Web site, a Japanese Twitter feed, a Japanese mobile site, a Japanese Instagram account, a Japanese LINE blog, and a Japanese YouTube channel. If you use KakaoTalk, you can add them as a Plus Friend, and Block B also has a channel on V App.
A number of fan groups translate Block B material into a variety of languages. (And a big THANK YOU to all those hardworking BBCs!)
For other languages:
BBC Mexico translates into Spanish
Block B Brazil translates into Brazilian Portuguese
Block B Romania translates into Romanian
Block B Poland translates into Polish
7BUSTERVN translates into Vietnamese
Block B Thailand translates into Thai (ภาษาไทย)
Block B FAMILY translates into Chinese (中文)
ArabBBC translates into Arabic (العَرَبِيةُ)
Block B * The 1st Russian & CIS Fanbase translates into Russian (русский язык)
Block B Hungary translates into Hungarian
There are more international fan groups out there! Block B International has a list of fan groups by country, so look there.
If you want to try puzzling out the Korean Tweets (Twitter has an auto-translate button!), here are links to the various members' Twitter accounts:
They also have Instagram accounts:
For general background information on the group, there's always Wikipedia (the Block B discography article has chart rankings and the like). Wikipedia also has an article on K-pop culture that can help outsiders understand what it is that Block B is constantly mocking.