EVE Online testers on Singularity have already had a sampling of the DirectX 11 client, but other players will have a chance to try it out when it releases with the Rubicon expansion next month. Once the update goes live, players with an OS and GPU that supports DirectX 11 will have it automatically enabled while those that do not will continue to use the DirectX 9 client, but you can switch between the two if your system supports both versions. CCP also provided a brief list of answers for frequently asked questions in their latest dev blog.

• Can I choose between DX9 and DX11? The Launcher will soon have a setting where you can toggle this (if your GPU does not support DX11, this checkbox will be disabled or missing).
• Are you sunsetting DX9? No, and we have no plan to.
• Does this affect the Mac? No, Mac will continue to use DX9.
• Do I have to download two clients now? No, we just ship a DX9 and DX11 version of our rendering engine (Trinity) and choose between them at runtime.
• Is the minimum machine spec changing? No, the minimum spec machine does not support DX11 and will continue to use DX9.
• My client is using DX11 but looks the same, what gives? Our DX9 and DX11 clients should look the same. No new features. Yet.

EVE Online: Rubicon is scheduled to launch on November 18th, 2013.

Source: EVE DirectX 11 Blog