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I’ve used Deliveries by Junecloud for several years now. One of my favorite apps as I track a lot packages. Colorful, easy to use, updates very fast upon delivery, if you copy a tracking number and open Delieveries it immediately recognizes your shipment by carrier and prompts to add it to you tracking list. Also rated 4.9 out of 5 on the App Store.

Oh...there’s also a Mac app...and a Junecloud iCloud so adding a shipment will appear on all your devices. Best I’ve used...

Added: Also an Apple Watch app which can be handy.
 
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I’ve been using Aftership for a couple of months now.

Free and with Android-iOS sync.
 
I’ve used Deliveries by Junecloud for several years now. One of my favorite apps as I track a lot packages. Colorful, easy to use, updates very fast upon delivery, if you copy a tracking number and open Delieveries it immediately recognizes your shipment by carrier and prompts to add it to you tracking list. Also rated 4.9 out of 5 on the App Store.

Oh...there’s also a Mac app...and a Junecloud iCloud so adding a shipment will appear on all your devices. Best I’ve used...

Added: Also an Apple Watch app which can be handy.

+1 for Deliveries. Been using it for over a year now, and you can't beat it.
 
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17track, chinees company, but tracks everything. I'm not sure about instant notification but it's the only one for me that always was able to track all of my packages.
 
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