We have extended the timeframe for the transfers to the Oceanic realm Gundrak. These transfers will close on Monday, December 8, at 12:00pm PST (December 9, 7:00am AEDT). We are also including the PvE realm Saurfang as a source realm to ensure those who wanted to play on a PvP server can continue to do [...]

Bornakk has announced some new policy with paid character transfers (Source)
We are reducing the time restriction on Paid Character Transfers (PCTs) to newly opened realms. As of today, players will be able to transfer characters to a new realm after the realm has been live for 90 days. This limit does not apply to PCTs [...]

We will be offering free character moves from selected high population realms to lower populated realms, assisting in population dispersal. The ability to move a character on the selected source realms will become available on Friday, April 18 at 12:00PM PDT, and are scheduled to run until Friday, April 25 at 12:00PM PDT.
This round of [...]

Here’s the post from European CM Vaneras about the available free character migrations. (src)
Due to population differences between some of the highest and lowest populated PvP realms, the following Free Character Migration will be available from April 16th to 22nd:
From: Crushridge, Outland, Burning Legion, Stormscale
To: Burning Blade, Haomarush, Dentarg
From: Warsong
To: Stonemaul
Please note that the migration [...]

We are working to address an issue affecting both the Paid Character Name change and Character transfer service, as they are currently unavailable. We’ll provide an update as soon as these services have been restored. Thank you.
Update: These services should be working once again. Thank you for your patience.[ Post edited by Eyonix ] [...]