Think of homerunhd as simply a decoder. By itself it simply allows you to translate the feed from the antenna to a digital source. The interface is up to you, although you can use their free software on a computer.
We are using Apple TV with the Channels app. You can pause live TV and fast forward. The picture quality is excellent. You can use a beta DVR however we are not doing my that since so much of what's on is available through other sources if you miss it live.