While there have been plenty of third-party options available for connecting iOS users to their Outlook accounts, there has never been an official app from Microsoft. It's an oversight that has finally been corrected with the Outlook Web App (OWA) for iOS.
The app is being released in two different native versions, one for iPhone and one for iPad. OWA for iOS connects to the email, calendar and contacts of Office 365 for business subscribers, giving them complete access to their Outlook on the go. Beyond those basic tools, the app features push notifications and a powerful voice search that can access your contacts or bring up your calendar.