Update: As of version 1.1, you've had the ability to select the location of the Rekordbox analysis data yourself; note that the analysis data is NOT the Rekordbox database. The information below still applies to moving / copying your database.
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Do you use multiple computers or need to move your Rekordbox database because you're upgrading your computer? Or do you simply want to make a snapshot-backup of your database? This is the guide for you!

Before you start, I should point out that this database move relies on the fact you'll have the files (your music) in the same location at the destination as you do at the source. 

Translation:

- if you keep your music on an external drive and it uses the same drive letter (Windows) on each computer, you're fine

- if you're using the same operating system on each computer and keep your music files in the same location on each (regardless of internal or external storage), you're fine

- if you're using two different operating systems and you keep your music in your "My Music" folder (or other system-based folder), it MAY not be available on the other computer

The next thing is you need to ensure that both computers have the EXACT same version of Rekordbox installed. If this means you need to over-install just to be sure, do so. You can download the latest version from the Rekordbox support site.

If you have just installed from scratch, launch the software and enter your installation key for validation then quit the program.

If you have just upgraded, open the software once and then close it.

On your old computer, browse to the following location to find your Rekordbox files. Note that you may need to unhide the hidden / system folders in order to see these files and folders. For information on doing that for your specific OS, please Google.

XP: C:\Documents and Settings\yourusername\Application Data\Pioneer\rekordbox

Vista: C:\Users\yourusername\AppData\Roaming\Pioneer\rekordbox 

7: C:\Users\yourusername\AppData\Roaming\Pioneer\rekordbox

OSX: /Users/yourusername/Library/Pioneer/rekordbox

Open that folder and you will find:

Crashes (folder)
PIONEER (folder)

datafile.backup.edb
datafile.edb
dummy.edb
license
rekordbox.settings
Upmgr rekordbox.settings

Copy everything EXCEPT The license file to a temporary storage medium in order to transfer it over to the other location.

Navigate to the database location on the destination, but first open the rekordbox folder and create a new folder inside, call it "Old Files". Copy and paste everything EXCEPT the license file into this folder.

Finally, copy the database from the temporary storage medium into the destination rekordbox folder.

Open the new Rekordbox and (if you did everything correctly) all your preferences will have been retained, you should see your library and be able to play the tracks.

If you have any questions about this procedure, please ask and we can provide assistance.