When using the add media button in the CKEditor in our Drupal 7 installation, and then clicking the Library tab, this is the dialog that we get:

What we would like is the ability to have filters etc. like in this screenshot from the Drupal Media Module page:

So far we are unable to figure out how to configure the media module to have this extra View Library option.
We’d also like a similar function for when users click on the link button in the CKEditor.
Thanks
The screenshot is from the (unstable) 2.x branch. The changes between 1.x and 2.x are documented here, one of them being:
Bottom line, if you want that functionality you’ll need to install the unstable branch of the module (although I really wouldn’t recommend doing that, not a lot of modules get marked as ‘unstable’ so you should use any one that is with extreme caution).
I don’t think there’s any (existing) way to force the standard CKEditor link button to use the media popup, as it’s provided by the CKEditor module itself. I think you’d need to write a custom plugin for both CKEditor and Media to get that functionality.