Hey Les,
Both, i suppose, but I was looking for backing tracks for practicing. Headphone into a computor or amp.
For silent practicing without backing tracks, I just use my amps with a Mesa Cab Clone that has a headphone jack. With that I use headphones that have their own built in amplifier made by Blue. The output level of the Cab Clone for headphones depends on the amp setting, so to avoid that issue altogether, I use the Blue headphones - they're very good cans by the way, I also use them for studio work and travel.
I've also plugged it into a computer interface and gone that route when I want to practice with backing tracks - however I create my own backing tracks in Logic or Digital Performer. I use a Universal Audio Apollo interface, which is a good one, but there are a lot of choices on the market in every price range.
Any computer DAW will get you there, you simply need an interface for your guitar input and headphones.