Outlook Anywhere is a special service that allows Outlook clients to connect via SSL/HTTPS protocols to their mailboxes from remote locations. Previously this method was known as RPC-over-HTTPS, but it was renamed into Outlook Anywhere in Outlook 2013, Outlook 2010, or Outlook 2007.
The main advantage of Outlook Anywhere is that normal Outlook requests are "hidden" in HTTPS, and thus they are able to pass through firewalls via standard SSL/HTTPS ports (so no need to open special RPC ports).
Another attractive aspect of Outlook Anywhere solution for individual users and companies is that it is not required to create a VPN connections. All that is needed is open 80 and 443 ports (these ports are usually open for other web applications).
Selecting of Authentication method will depend on several factors.
There are several innovations introduced in Exchange Server 2010:
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