Back in 2015, William Scott Phillips and Suzanne Schmidt Phillips, an American couple, decided to sue Apple for not explaining the Wi-Fi Assist feature well enough. They alleged that they incurred much higher mobile data costs than they expected because Apple didn't mention or 'downplayed' the fact that Wi-Fi Assist could feast on their precious 3G data.
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As per Apple's support page, "With Wi-Fi Assist, you can stay connected to the Internet even if you have a poor Wi-Fi connection. For example, if you're using Safari with a poor Wi-Fi connection and a webpage doesn't load, Wi-Fi Assist will activate and automatically switch to cellular so that the webpage continues to load. You can use Wi-Fi Assist with most apps like Safari, Apple Music, Mail, Maps, and more.
Because you'll stay connected to the Internet over cellular when you have a poor Wi-Fi connection, you might use more cellular data. For most users, this should only be a small percentage higher than previous usage."
So in case you're using data-heavy apps like Music streaming service, FaceTime, Maps or even downloading apps and updates from the App Store, you may end up paying dearly for being around a poor Wi-Fi connection, unless you're careful enough to turn off the Wi-Fi Assist feature or you have enough cellular data to handle your internet usage.
Turning off Wi-Fi Assist is simple. Once you go to Settings, click on Cellular, then browse down until you spot Wi-Fi Assist at the bottom. There's a sign next to it which will indicate if the feature is turned on or off. If you need it, then keep it turned on or turn it off if you have limited cellular data and are fine with slow broadband speed.
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Wi-Fi Assist in Settings will also show the amount of cellular data consumed in a given period of time. The date and time from when the consumption is being tracked is mentioned below the 'Reset Statistics' key. If you click on Reset Statistics, then the consumption will come down to zero and will start tracking cellular consumption again until you reset it again.
Apple has introduced several updates to Wi-Fi Assist over the years and now the feature is very user-friendly and easy to understand. The feature doesn't consume cellular data when you are in a roaming zone nor does it consume cellular data to support internet usage by background apps. You would also know when the feature is active and consuming cellular data because when it does, the Wi-Fi symbol will disappear from the status bar.