iPhone Dev team released Redsn0w 0.9.8b3 for iOS 4.3.4 to jailbreak iPhone, iPadand iPod Touch. But it supports only a tethered jailbreak, which means that you need to connect your iOS device to the computer on every reboot. iPhone hacking expert Stefan Esser who goes by the Twitter handle i0n1c, credited for developing the untethered jailbreak

Read more:
Apple Fixes Untethered Exploit In iOS 4.3.4; So Don’t Expect Untethered iOS 4.3.4 Jailbreak To Be Released Anytime Soon

In other news:

iOS 4.3.3 Doesn’t Fix Untethered Jailbreak
The iOS 4.3.3 software update Apple recently released does not fix the untethered jailbreak exploit used in iPhone hacker, i0n1c’s jailbreak. This has been confirmed by iPhone Dev Team member @comex . This means

Untethered Jailbreak Exploit May Be Patched In iOS 5
Yesterday, we reported that iOS 5 was successful jailbroken by the iPhone Dev Team less than 24 hours after it was released using the limera1n exploit. But MuscleNerd had revealed that the jailbreak is currently tethered,

iOS 4.3.3 Already Jailbroken; Untethered iOS 4.3.3 Jailbreak Could Be Released Soon
It has hardly been a few hours since Apple released iOS 4.3.3 for iPhone, iPad and iPod Touch and we’re already hearing reports that the latest iOS software update can be jailbroken using Redsn0w released by the iPhone Dev team to jailbreak

Untethered Jailbreak For iOS 5 May Be Released Soon
If you were planning to skip jailbreaking iOS 5 because currently only a tethered jailbreak available then there is some good news for you. iPhone hacker – Stefan Esser – better known by his Twitter

Untethered Jailbreak For iOS 4.3 In Alpha; Seas0nPass To Jailbreak Apple TV 4.2 (iOS 4.3) Released
It didn’t take the iPhone hacking community a long time to jailbreak iOS 4.3, which was released yesterday. YouTube user with the handle xpl0n1c has published a video, which shows a jailbroken iPad running iOS 4.3