The best hypotheses, IMO, begin with certain mineral surfaces acting as the catalysts for polymerisation. Bentonite clays and phosphate minerals in particular are used by synthetic chemists even today. The repetitive atomic structure of these surfaces (they're effectively crystalline lattices) act to line up particular precursor molecules, helping them to react with each other. Hit the right set of conditions, and you'll find yourself churning out polynucleotides.
There are some very involved theories based upon this central idea, and what I think is some quite compelling evidence in the way cell metabolism works. Quite a lot of the processes are really quite weird and make little sense from a design perspective, but become relatively clear when you keep in mind that evolution only works by successive slight modifications of what went before (kludges upon kludges, rather than tearing down and rebuilding). Been ages since I've read about any of it so I'm not up to date, but I do recall it makes fascinating reading.
