So please consider this post as outdated and refer to the official symfony templating documentation and related cookbook articles.

For myself i would always prefer writing a twig extension in favor of depositing globals into the “twig”-section of config.yml.

have a look at this cookbook entry how to do things properly:
http://symfony.com/doc/current/cookbook/templating/global_variables.html

Example:

public function getHttp()
{
if ($request = $this->getRequest()) {
return $request->getHttpHost();
}
}

use {{ app.http }} in your Twig

Thanks for pointing out the GlobalVariables.php file though!

The master of the internet told me to do so, but never reported back since then :(

Perhaps i decide to translate the article in the near future, in the meantime i suggest to investigate the contents of the class Symfony\Bundle\FrameworkBundle\Templating\GlobalVariables which should make things clear.