There are known issues with Apple's native mail app and Office 365, particularly with iOS 10, so we recommend using Microsoft's Outlook app on your iPhone or iPad instead.

Installing

Go to the App Store on your device, download and install the Outlook app. It will look like this:

You may need to enter your Apple ID to download and install so have this to hand before you start. If you can't remember your Apple ID or password you can reset these here: https://iforgot.apple.com/password/verify/appleid

Tap on Get, then Install.  

Setting Up

Once the app is installed, open it and it will take you through the setup process. This will ask for your Office 365 email address and password so have this to hand.

Tap Get Started:

Enter your email address and tap Add Account:

Your account will be checked:

If the account is found, you can then enter the password:

If the password is correct the account will set up and you will be asked if you want to add another. Choose Maybe Later:

Choose whether you want Outlook to notify you of emails and events:

You can now step though a short intro, or tap Skip:

You can turn off the Focused Inbox and other options by tapping on the Settings cog at the bottom of the Outlook screen: