In reply to Will Cat:
It's solo in the sense that you climb alone (no partner) but not in the sense that there is no rope.
The most usual way to do this is to anchor one end of the rope at the bottom of the pitch, and then clip yourself into the rope using some kind of rope soloing device. I've used a death modified grigri* before, but there are dedicated devices out there now (Silent Partner etc.). The grigri usually needs a chest harness, and whilst it is hands free, the rope does not feed as easily as it would do if one was belayed conventinally**.
You place gear below the device, which will lock if you fall off. Once you've reached the top you then need to abseil the pitch to strip it, and then jug or self-belay back up the rope to get to the top again. This system works really well for solo aiding, but it a little cumbersome for free climbing where finding a partner or just soloing the damn thing are probably easier.
For alpine or mountain soloing you can also use a much cruder system with a shorter length of rope. Here you can tie into both ends of the rope, and then clip or thread it through a runner (ideally an in situ one e.g. peg) just below a hard step. You climb the step with a big loop as your safety net, and then once above it untie one end to pull the rope through, leaving the runner behind. I've always called this a 'Pakistani Death Loop' but I've no idea where I got that from so it may be a wholly unsuitable or incorrect name.
Hope that helps.
* Death modified in that the flap is filed off so that, when you rig it upside down on a chest harness the rope feeds much more easily. If you google 'death modified grigri' there are several sites which show you how to do it. I'm not going to tell you!
**I will also add that you shouldn't need to carry the rope in a sack for shorter pitches, it will feed alright and the weight of the 'dead' rope will stop the weight of the 'live' rope from self-feeding you yards of slack. If this happens another option is to clove-hitch the live rope into a good runner as you pass, increasing your fall factor but stopping the dreaded 'self-feed'!