To access an Outlook account on your iPhone, use either the native Mail app or Microsoft's own version of Outlook for iOS devices. How you go about setting up your Microsoft Outlook account varies slightly depending on which of these two solutions you choose.
Use the Native iOS Mail App
Open the Settings app on your iPhone and select Mail, Contacts, Calendars.
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Choose Add Account on the main Mail, Contacts, Calendars screen.
Depending on the number of accounts currently set up for use on your iPhone, you may have to scroll down to locate the Add Account button.
Select Outlook.com as the account type on the Add Account screen.
Enter your name, full Outlook email address and your Outlook account password in the provided fields. Tap the Next button in the top-right corner when you are finished to complete the account setup.
After you set up your Outlook account using the Settings app, tap the Mail icon on the iPhone's home screen to access the Mail app. Select your Outlook account on the Mailboxes screen to display your Outlook inbox. Here you can check for new mail, send messages and access many of Outlook.com's other email features.
Use the Microsoft Outlook App
Open the App Store on your iPhone and search for the Microsoft Outlook app. Open the app's details page in the App Store, tap the Free button and follow the prompts to download and install the app on your iPhone.
Open the Microsoft Outlook app after the installation completes and select Add Account.
After you add the first account in the Outlook app, tap the Settings icon in the top-right corner of the main screen and select Add Account to add subsequent email accounts.
Choose Outlook.com as your account type.
As with the desktop version of Outlook, you can also use the Outlook app for iOS devices to manage non-Microsoft email accounts, including Gmail, Yahoo Mail, Exchange, iCloud and any IMAP-based email account.
Enter your full Outlook email address and associated password in the provided fields and then tap the Sign In button.
Tap Yes to confirm that you want the Outlook app to synchronize your messages and other data.
After you set up your account, tap the Mail icon on the menu along the top of the screen to check for new mail and to send messages. For additional tips on using the iOS version of Outlook, visit Microsoft's Frequently Asked Questions page.
Outlook Web App
If you use the Office 365 platform, there is an iOS version of the OWA for iPhone app you can install on your iPhone to access your account. The app is a free download from the App Store, but you must be subscribed to the latest version of Office 365 for Business in order to use it.