For the thousands of us who use WhatsApp daily, nay hourly, the app has become a pseudo repository for our digital lives. It has addresses our friends texted us, meeting dates, social plans, important notices from our bosses or coworkers, pictures of our kids or relatives, cute audio blurbs from our loved ones, and so much more. Although the app has a search function, that isn't the optimal way to find a specific message: you may not remember the exact words used or you may simply be looking for a media file that can't be found using the search function.

Starring those important messages makes a lot of sense and I'm surprised I never thought how much this feature could be useful until I started using it in today's update. Version 2.12.337 of WhatsApp introduced the option, then was quickly followed by what must be a small bug fix in version 2.12.338.
In short, message starring works like you expect it to. Tap and hold on any message(s) and you'll see a new star icon in the app's toolbar. Tap that and a small star appears at the bottom of the message, next to the timestamp. To remove it, tap and hold again and you'll get a crossed star icon that takes care of it.
whatsapp-star-option-1 whatsapp-star-option-2
Starred messages are accessible from the app's overflow menu. They show up in a scrollable timeline with the sender's name, date, and the full content. That also applies to media files of all kinds: pictures, videos, and audio. You can unstar messages from this view too.
whatsapp-star-message-3 whatsapp-star-message-4 whatsapp-star-message-5
The feature was added to the iOS counterpart of WhatsApp about a month ago, so it's a little late coming to Android. But it seems to be working well even as a beta iteration. Until it graduates to the Play Store's stable version, you'll have to manually grab the APK in order to enjoy it.
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