This post attempts to describe the line of reasoning that inspired the recent effort on my advanced F2L page. I held off writing this up then to avoid cluttering that thread, but it seems more appropriate now, after Feliks's new WR average, as several people mentioned the "style of the future." Let me know whether or not you're convinced.
A little background. While I was in Europe this spring, a number of cubers remarked on my unique fingertricks. My fingers stay very close to the cube, and I often use not the tips but more inner parts of my fingers. During the F2L, I frequently use double layer turns, tilts (often to left cross), or even some wrist turning. For example, instead of LU2'L'U'LUL', I often tilt the cube slightly to x' and z while moving my whole right hand to hold the BUL sticker with the index, FU with thumb, and BU-BUR with the rest; do L with the right index while moving the whole left hand to hold the B center with thumb and F with the rest; pull back the left hand for Dw2'; then continue with right-handed R'U'RUR'.
I started speedcubing in 2002. Back then, since there were less F2L algorithms that avoided whole cube turns (no R'FRF'RU'R' or R'FRF'R'U'R yet), the faster tilts and double layer turns were natural ways to speed up the F2L. Since double layer turns also help with recognition, I took this to an extreme as in the example above to smoothen my F2L. Another explanation is that cubes from this period POPed when turned too fast with a slight inaccuracy. I avoided the problem altogether by concentrating on UR turns. While I don't think that other top cubers through 2006 used double layer turns to this extent, many of the first sub-15 cubers used an F2L style consistent with the slogan, "go slow, and look ahead."
Then, in 2007, came the Japanese cubers (because I don't really count).* They used whole cube turns. They had a choppier F2L. And they turned fast. Their F2L almost seemed to be pairs being "processed" one after another--in a way, not unlike OLL/PLL. Turning speed and lookahead are the two ever-conflicting essences of F2L. My impression is that the majority of top cubers since 2007 have stressed the former at a slight cost of the latter, with spectacular success; rather than gradually increasing the turning speed while maintaining a complete lookahead, turning speed now drags along lookahead.
(*I'm obviously greatly simplifying the story here by skipping over a number of major historical cubers. Perhaps there was a gradual shift towards the eventual evolution that I describe. Honestly, I haven't carefully watched enough videos from this period to judge.)
The recent development in hardware certainly supports this evolution. With anti-POP mechanisms and lighter cubes, today's top cubers are better equipped than ever to pursue increasingly high tps. Whole cube turns, which once helped to solidify lookahead, are now the biggest hindrance to turning speed. For some F2L cases, the problem has already been solved: U'L'ULDwRU'R' was first replaced by R'FRF'RUR', and then by F'RUR'U'R'FR. But even for this case, different starting angles and target slots still often require a whole cube turn.
It was under such considerations that I set out to compile a collection of rotationless F2L algorithms. To address the issue, I needed to consider every target slot for each pair pattern, plus AUFs as appropriate. Thus, for pair pattern V1 to target slot FL, I noted the old but not often used FRU2'R'F' and also proposed (U2)FLw'ULwF2' (with left index push for the first F) as an alternative to the traditional (U2)yRUR'URU'R'. As for empty-slot cases, Joël's recent contribution of RU2'R'UR'U'R demonstrated that there were even simple alternative reductions waiting to be found. After adding mirrors and rotations of existing F2L tricks from various sources, I explored variants of existing algorithms for as yet undocumented ones. The result is what should be a fairly comprehensive list that I myself have yet to sift through.
My list is not meant to be a final word on F2L. Rather, it is made as thorough as possible so that the community can judge the merits of each algorithm, comparing with traditional ones. It is also meant to encourage further explorations; to this end, the right index push for F' should be essential to many fast rotationless algorithms. It is my strong belief that a thorough review of F2L, optimizing algorithms for the new style, should be one of the main tasks for today's CFOP community.