iOS: Email and to-do apps on the iPhone aren't difficult to come by, but Swingdo and Swingmail work together really well. The apps support multiple email and calendar services to give you one place to manage your email and to-dos, and to see what appointments you have coming up.
The video above shows you how Swingdo works, and the one below gives you a quick tour of Swingmail before you give them a try (both apps are from Japanese developer BHI, so excuse any awkward English). Swingmail supports Gmail and Google Apps, Microsoft and Outlook accounts, Yahoo, iCloud, and more, and even connects to Twitter, for those of you who use it to stay in touch with friends as much as email.
Swingdo automatically connects to your calendar (and to Swingmail) so you can turn emails into actionable to-dos and reminders, and that any calendar appointments you have float up on your to-do list. You'll get reminders, and the app supports the Apple Watch, so you'll get notifications on your wrist too if you own one. Swingdo uses context from your emails, appointments, and Twitter messages to schedule those to-dos, complete with titles, descriptions (that you may want to edit,) and the location associated with the event. When you're done with the event or to-do, just swipe to dismiss it.
At the end of the day, you can use one app or the other, but they both work so well together it helps to try out both and see if it can replace the email or to-do app you're currently using. The best benefit is that when it's all set up, you'll have one steady stream of all of your to-dos, calendar appointments, and more, pulled from all of your different email addresses, which is a huge improvement over switching calendars to see specific events. Hit the link below to check it out.