With the recent announcement from Tumblr, many blogs are looking for places to move their history to. WordPress is one option, and the Tumblr Importer plugin makes that easy.
There is one gotcha. The import itself is done by a WP-Cron job, and that doesn’t work correctly on some server setups. This means that you will need to create a cronjob on the server (if using hosted WordPress) to run it.
On your server, in the shell,
First, create the directory for the output
Then, in your crontab
*/1 * * * * curl -I http://YOUR_SITE_URL/wp-cron.php >> $HOME/tmp/out 2>&1
The cronjob will now be called every minute and, depending on how far back your blogs goes, be imported in a few hours (plue/minus longer).