There is no Jailbreak for iOS 10.2.1 → 10.3.2 Beta, don't update!
iOS 10.2 is no longer sigend, so you can't update / downgrade to it and Jailbreak.

Current Jailbreak Status

iOS  Version: Jailbreak Status: Jailbreak Tool: Jailbreak Tool Availability
iOS 10.3.2 Beta No Jailbreak! Don't update!  No Jailbreak No Jailbreak
iOS 10.3.1 No Jailbreak! Don't update!  No Jailbreak No Jailbreak
iOS 10.3 No Jailbreak! Don't update!  No Jailbreak No Jailbreak
iOS 10.2.1 No Jailbreak! Don't update!  No Jailbreak No Jailbreak
iOS 10.2 Yes! Yalu Jailbreak Yalu Jailbreak iPA (Linux, Windows, OS X) Only x64.
iOS 10.1.1 Yes! Yalu Jailbreak Yalu Jailbreak iPA (Linux, Windows, OS X) Only x64.
iOS 10.1 Yes! Yalu Jailbreak Yalu Jailbreak iPA (Linux, Windows, OS X) Only x64.
iOS 10.0.2 Yes! Yalu Jailbreak Yalu Jailbreak iPA (Linux, Windows, OS X) Only x64.
iOS 10.0.1 Yes! Yalu Jailbreak Yalu Jailbreak iPA (Linux, Windows, OS X) Only x64.
iOS 10.0 Yes! Yalu Jailbreak Yalu Jailbreak iPA (Linux, Windows, OS X) Only x64.
iOS 9.3.5 No Jailbreak! Don't update!  No Jailbreak No Jailbreak
iOS 9.3.4 Yes! Home Depot Jailbreak Home Depot iPA (Linux, Windows, OS X) Only 32-Bit
iOS 9.3.3 Yes! Pangu Jailbreak (x64) Pangu / Home Depot Windows / iPA (Linux, Windows, OS X) Only 32-Bit
iOS 9.3.2 Yes! Pangu Jailbreak (x64) Pangu Windows
iOS 9.3.1 Yes! Pangu Jailbreak (x64) Pangu Windows
Apple TV (tvOS 9.0.2) Yes, with Pangu for tvOS Pangu for tvOS version 1.0 tvOS (Apple TV)
iOS 9.3 Yes! Pangu Jailbreak (x64) Pangu Windows
iOS 9.2.1 Yes! Pangu Jailbreak (x64) Pangu Windows
iOS 9.2 Yes! Pangu Jailbreak (x64) Pangu Windows
iOS 9.1 Yes, Pangu Jailbreak Pangu 9 [MAC] or [Windows] (Fast Mirror) Both OSX and Windows
iOS 9.0.2 Yes, Pangu Jailbreak Pangu 9 Both OSX and Windows
iOS 9.0.1 Yes, Pangu Jailbreak Pangu 9 Both OSX and Windows
iOS 9.0 Yes, Pangu Jailbreak Pangu 9 Both OSX and Windows
iOS 8.1.3 to 8.4 Yes, TAIG Jailbreak TAIG v2.4.5 Both OSX and Windows
iOS 8.0 to 8.1 Yes, Pangu Jailbreak Pangu 8 Both OSX and Windows
iOS 7.1.2 Yes, Pangu Jailbreak Pangu 7 Both OSX and Windows
iOS 7.1.1 Yes, Pangu Jailbreak Pangu 7 Both OSX and Windows
iOS 7.1 Yes, Pangu Jailbreak Pangu 7 Both OSX and Windows
iOS 7.0 to 7.0.6 Yes, evasi0n Jailbreak evasi0n 1.0.7 Both OSX and Windows
iOS 6.1.3 to 6.1.6 Yes, p0sixspwn Jailbreak p0sixspwn tool Both OSX and Windows
iOS 6.0 to 6.1.2 Yes, evasi0n Jailbreak evasi0n 1.5.3 OSX, Linux, Windows
iOS 5.1.1 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 5.0 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 4.3.5 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 4.3 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 4.2 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 3.2.2 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 3.1.2 to 3.2.1 Yes, JailbreakMe Star (2.0) JailbreakME Star 2.0 Open in Safari on iOS
iOS 3.0 Yes, Redsn0w Jailbreak Redsn0w B3 Both OSX and Windows
iOS 2.x Yes, Pwnage Tool Jailbreak Pwnage Tool OS X Only
iOS 1.0 Yes, iBrickr Jailbreak iBrickr Jailbreak Windows