OWA for iPhone and OWA for iPad are native iOS apps which provide everything you get in the browser-based Outlook Web App, and more.
The apps are business-oriented, and require a subscription to Office 365 that includes the latest update of Exchange Online before you'll be able to use them.
If that sounds like you, though, there's a lot on offer here, with all the email, calendar and contact functionality you'd expect from Outlook Web App. You can compose, send, receive and manage emails, view and update your schedule, create and manage events, access your contacts and more.
The fact that you're now using a native app means you also get some valuable extras. OWA for iPhone/ iPad stores your credentials, for instance, so that you're automatically logged into the device. And it can actively keep you up-to-date, notifying you of new emails and popping up meeting reminders, even if the app is closed.
This integration brings some brand new features. You can now send emails or set up meetings through voice commands, for example, and your OWA contact details will be recognised and used by the iPhone's caller ID function.
And if you're worried about all this power falling into the wrong hands, Microsoft has that covered, too: a remote wipe capability can delete email and calendar data if your device is lost or stolen.