raster to vector?

[Strapping Young Lad]

I'm not sure if this belongs in "Technophile talk," but here I go. How would one convert a raster-based image to vector? I was advised by a website to "purchase" Adobe Streamline but the program seems pretty out of date. I vaguely recall a way to do it in Illustrator, but my memory does not serve me well in this particular instance. I'm sure there's a technique to this that's currently over my head, too. Can anyone help with my life-shattering dilemma?