For 12 years, the mDNSResponder service managed a surprisingly large part of our Mac’s networking, and it managed this task well. But as of OS X 10.10, the mDNSResponder has been replaced with discoveryd, which does the same thing. Mostly.
Some of the bugs in Yosemite discussed in an article linked last week seem to have origins in moving from mDNSResponder to discoveryd. Here is an explanation of what specifically is not working, and how to fix it. However, it is not for the faint of heart: you can potentially leave your Apple in an unbootable state, and who knows what will happen when an update is installed.