Mobile devices are an integral part of the business environment. Employees are using their devices for web browsing, personal email, corporate communications and much more.
Office 365 supports the native ActiveSync features and policies of Exchange Server 2010 Service Pack 1, including:
The Exchange Active Sync protocol is licensed to a lot of licensees, including Apple and Google.
Mobile Device Management Tools by Microsoft
Should you want to extend the above with e.g. management of mobile applications from an Application Catalog consider looking into System Center 2012 Configuration Manager or the Windows Intune service. They both enable mobile device management in Office 365 via the Exchange Server connector, supported by Exchange Online (Office 365)
In general, third-party applications can integrate with Exchange Online if they utilize the Exchange Web Services API and do not require software or hardware to be installed in the Exchange Online datacenter. Applications that uses the Exchange Server MAPI/CDO API, which is not available in Exchange Online obviously doesn’t work. Microsoft does not test or certify applications for use with Exchange Online.