A security researcher discovered a vulnerability in the Android MMS system which could be exploited to control Android phones without the user doing anything. It was reported to Google in April and a patch was release.
Unfortunately, as is the case with most manufacturers, the Android system rarely gets more than one or two upgrades.
The vulnerability affects Androids 2.2 to 5.1.1 which is the majority of smartphones currently in use.
To reduce the risk of being exploited you should disable MMS auto-retrieval in you SMS app, Hangouts app, and any other apps that deal with your SMS & MMS. To do this go into the settings of each app and disable MMS auto-retrieval. See the images below as a demonstration as well as the link at the end of the post.
For more on the topic and to stay updated follow the topic on Quora and these threads & articles:
Stagefright Android MMS Vulnerability (July 2015): What is Stagefright Android MMS vulnerability?
How do I protect my Android phone from the Stagefright vulnerability? FAQ
How To: Protect your Android device from the MMS-hack (Stagefright exploit)
Ibrahim El Merehbi 