Q Can I connect my Xbox 360 to my iMac 27” (2011 model), to use the latter’s display?
A Only certain versions of the iMac from late 2009 to mid 2014 can operate in Target Display mode, in which they will show digital video input through their Mini DisplayPort or Thunderbolt port.
Your Xbox must be a more recent model with HDMI output, for which you will need a fairly expensive adaptor that will convert between HDMI and Mini DisplayPort. There is controversy over which adaptors will work reliably, but Belkin used to offer its AV360 aimed specifically at this combination of hardware, so that may be your best starting point if you can find one.
You also need to ensure that your iMac is brought fully up to date with firmware patches. Once you have assembled your hardware, follow Apple’s step by step instructions, and you should then be able to enjoy the video output from your Xbox on the gorgeous display of your iMac. User reports occasionally claim this does not work, so you should ensure that you can return the HDMI to Mini DisplayPort adaptor for a full refund, just in case.
Updated from the original, which was first published in MacUser volume 28 issue 11, 2012.