I was in the presentation launch of the OWA for ios devices and boy, does that look exciting! We now feature a full app for Office 365 supporting OWA offline and many more options. Support for Exchange 2013 on premise deployments is not there yet but is planned to come soon (when it's ready!)

"Our goal is to help our customers remain productive anytime, anywhere.  This includes providing a great email experience on smartphones and tablets.  Windows Phone 8 comes with a top-notch native email client in Outlook Mobile, and we offer Exchange ActiveSync (EAS), which is the de-facto industry standard for accessing Exchange email on mobile devices.  In order to better support many of our customers who use their iPhones and iPads for work, we are introducing OWA for iPhone and OWA for iPad, which bring a native Outlook Web App experience to iOS devices!"

Read more: http://blogs.office.com/b/office365tech/archive/2013/07/16/owa-for-iphone-and-owa-for-ipad.aspx