We most typically do this in the context of implementing a product like Cisco's Identity Services Engine (ISE). ISE uses 802.1x and has the ability to check clients for things like a certificate during the authentication / posture assessment / remediation process.
It also acts as a RADIUS server and can dynamically push out Change of Authorization (CoA) to the authenticator (i.e switch or Wireless controller) in order to control things like client VLAN assignment and any access-lists you may want to apply.
On the client side, a supplicant is used to interact with the authenticator. You can use native supplicants from OS X or Windows etc. but we generally recommend use of Cisco's AnyConnect Secure Mobility client with its Network Access Module (NAM) as it's much more full-featured for that purpose.
You could also do 802.1x with certificate authentication and use a different backend authentication server (like a regular Cisco ACS or Microsoft Network Policy Server) but you would just get more basic authentication vs. the rich functionality ISE gives (albeit ISE costs a lot more ;) ).
Have a look at this Youtube video for an example of setting up certificate authentication on ACS:
https://www.youtube.com/watch?v=U7qWJ7bIMHA
