I'm looking for the functionality described in this Wiki entry from 2009.
The article describes a tool that cuts a path to where an intersection is met. Is this or something similar a feature yet? If it is, where can I find it?
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Looks like someone has written about a concept for a tool. It doesn't exist in Inkscape yet.
It looks a bit like the Shape Builder tool in Illustrator. You can already do something kind of similar in Inkscape using the existing boolean operations.
I'll use one of the examples in your link.
Draw the circles with a stroke and no fill, and make sure they touch. Use snapping and guides to make sure it's accurate, then select them all and combine using Path > Combine.
Draw a rectangle around the circles, and fill it pink (or any colour you want), then Lower Selection to Bottom
Select both the rectangle and combined circles and do Path > Division. This will divide up all the pieces into individual closed paths (or shapes).
Select and delete the outer rectangle
Select two pieces on one side, and do Path > Union. Repeat for the two pieces on the other side
Select and change the fill of the individual pieces as required.
The page that you've linked seems to be just someone's concept for such a tool and is not actually implemented in Inkscape. Something like that is in development, however.
In the meantime, you'll have to use boolean operations that you can find under the 'Path' menu, or use the 'Boolean operation' path-effect.