A few months ago, Facebook was reported to be testing SMS integration in its Messenger app for Android. Now, that feature is officially live. It's entirely optional, so you'll need to enable it. To do so, head over to Settings in the Messenger app, select "SMS" and then choose "Default SMS app." This means all of your text messages will be sent and received on the Messenger app. Your SMS conversations will be in purple to differentiate them from the default Messenger blue.
Interestingly, SMS in Messenger doesn't support just text and images. It also supports rich content like stickers, GIFs, emojis and location sharing -- just like regular Messenger conversations. Facebook also wanted to clarify that none of the messages are stored on the company's servers; all of the text messages are sent via SMS as per usual. That does mean that regular texting fees do apply.
This feature is only for the Android app due to the limitations of iOS. But seeing as Apple's own Messaging is getting a lot of these Messenger-like enhancements -- emojis, stickers etc -- iPhone users probably aren't missing out too much.