The word from the jailbreak community is that a tethered jailbreak (the sort that you have to do again if you reboot, such as when your device crashes of the battery goes flat) for these devices is in the pipeline, and that an untethered jailbreak (one that will happily survive a reboot) is also in the works, although this may take longer.

FORBES: Can I Jailbreak My iPad 4/iPad Mini?

These devices can be jailbroken using a tool called Redsn0w, although that jailbreak is for now a tethered one.

FORBES: How Do I Jailbreak My iPhone 5?

To do this you need a tool called Redsn0w, although that jailbreak is, for now, a tethered one.

FORBES: Can I Jailbreak My iPad 4/iPad Mini?