Exchange's webmail - or OWA for Outlook Web App - can provide a reasonably close Outlook environment within the Internet Explorer web browser. A functional, though less identical experience, is also available within other browsers such as Mozilla Firefox, Google Chrome or Apple Safari. This experience is dubbed "OWA light".
What may have not been expected by those upgrading to Windows 8.1 for the first time - that is, those who did not venture to use the beta - is that under Internet Explorer 11 your Outlook Web App experience now renders as a second-grade citizen. Yes, it will be the OWA light experience.
This is not the first time this has happened; early adopters to Windows Vista experienced the same problem when trying to use Microsoft Exchange 2003 web mail, the fix requiring a patch on the Exchange server on that occasion.
The reason this is happening again is because Internet Explorer 11 no longer sends the "MSIE" (Microsoft Internet Explorer) token in the user-agent string which is part of the header information sent to a web server when a browser requests data. Exchange Server 2007, 2010 and 2013 evidently use this token to determine if the user is operating Internet Explorer; because the token cannot be found they assume not and thus present only the light experience.
There are some solutions; however, first, why did this happen? The answer is interesting and even shows some dysfunction between Microsoft's engineering teams.
According to a Microsoft blog the reason is that many web sites try to implement compatibility workarounds for Internet Explorer by "sniffing" the user-agent string for the MSIE value. If they find it, they operate different code. Internet Explorer 11 now sends a user-agent string which reads "Mozilla/5.0 (Windows NT 6.3; Trident 7.0; rv:11.0) like Gecko". This string is carefully and deliberately designed to make web sites interpret the IE11 browser as either WebKit or Gecko based, and not as "MSIE".
Microsoft's argument here is that Internet Explorer is no longer the evil old IE6 of the past which dismissed standards and required careful workarounds; it is instead a modern HTML-compliant powerful browser which churns through ACID tests with high results. Additionally, Microsoft's view is that many websites searching for the MSIE token are making compatibility problems for themselves and their users, and that fundamentally sniffing for a specific browser type is the wrong approach. Microsoft argues web sites should check for feature compatibilities, not for specific classes of browsers.
The consequence is the MSIE token is no longer presented - at least not by default; if a web page is rendered in compatibility mode within Internet Explorer 11 then the MSIE token will be sent - so this is one solution to the OWA webmail problem for Windows 8.1 users.
The irony here however is that Microsoft itself is apparently using browser detection to determine who is viewing webmail despite its own cautions that this is the wrong approach.
Nevertheless, this is why the incompatibility exists.
Administrators of Exchange 2013 servers can install a patch which resolves this problem; those using Exchange 2007 or 2010 servers will need to either use compatibility view or, somewhat unexpectedly, InPrivate browsing - which suggests the allegedly more secure browsing mode actually is more vocal about your web browser than the normal mode.
If you go the compatibility view route, use F10, View, Compatibility View to add your Exchange Server's webmail URL to the list of sites which automatically require this mode; you will then have the premium OWA experience again.