Microsoft just may have something here...
Microsoft recently released Outlook for iOS. Technically, it's a rebranding of acquisition Acompli, but it's still awesome. I've only been playing with it for a day, but it's already replaced both Apple's Mail app and the Calendar app on my iPhone and iPad. It works incredibly well with Gmail; mail, calendars, and contacts all sync perfectly so far.
There are two swipe gestures in email: left or right. Each is customizable. For me, it's swipe left to delete, and swipe right to postpone the message. Messages can be postponed for a predetermined amount of time, or you can customize when the message returns to your inbox. I've seen this functionality before on other apps, and I love it. There is a feature called Focused Inbox. I haven't figured out how the app decides what email is important, and what isn't, but it's easy to find messages even if they aren't deemed worthy for the Focused Inbox.
Everything else works as you'd expect. It's awesome to have mail, contacts, and calendars all in one app. Add to that the ability to attach documents from One Drive, Dropbox, or Google Drive, and Microsoft has a winner of an app here.
Why am I drooling over this app on the Photography blog? Because if you're running a photography business, you probably spend a good amount of time working with your inbox, calendar, and contacts. Outlook for iOS simplifies the process somewhat.
Now if they could just do the same for Outlook for OS X. That thing is still a hideous beast that refuses to play well with Google services.
Best part about Outlook for iOS? It's free, and it's in the App Store now.