Automatic background updates were introduced in WordPress 3.7 in an effort to promote better security and to streamline the Wordpress update experience. Here we examine how to do this manually and then also with a Wordpress Automatic Update Plugin
Wordpress Automatic Core Updates
If Wordpress is not updating 'out of the box' then manually setting up automatic Wordpress Updates for the core is very easy via wp-config.php:-
Wordpress Automatic Plugin and Theme Updates
Plugin and theme updates require a filter and "To enable or disable updates in all cases, you can leverage the auto_update_$type filter, where $type would be replaced with "plugin" or "theme"."
Wordpress Automatic Update Plugin
If the above seems like a hassle to you then you can gain full control of all your automatic Wordpress Updates via the Wordpress Easy Updates Manager Plugin. This will give you the full breadth of changes with basic radio toggle buttons.
This plugin also works with Wordpress Multisite.