iOS: Manual is a powerful, well-designed camera app that gives you total control over your photos' exposure, and with the arrival of iOS 10, Manual 2.0 can now shoot raw DNG photos. You've likely heard about the "raw" DNG files before as the preferred format among professional photographers. It's a lossless "digital negative" that retains more colour and tonal information than more compressed image formats like JPG, making it ideal for editing photos after the fact. iOS 10 enables recent iPhones to shoot raw photos, but Apple's native camera app doesn't actually give you the option; you need an app like Manual. You'll need an iPhone SE, 6S, 6S Plus, 7 or 7 Plus with iOS 10 to shoot raw photos.
Adobe Lightroom for iOS also recently gained the ability to shoot raw photos, but if you don't want to rely on the Adobe Creative Cloud infrastructure, Manual offers a more self-contained way to shoot and save your raw DNG photos. (As far as I can tell, you can't actually save a raw photo in Lightroom without exporting it as a JPG, unless you use Creative Cloud to sync your photos to multiple devices.) With Manual, you can just sync your photos to your desktop and then edit them in your preferred DNG-compatible software.
Manual ($5.99) [iTunes Store]