After my favorite pincer, there's a currently popular joseki line that I don't understand.

starts the joseki, at which point

and

are inevitable. In the pictured position, White
a followed by Black
b are the most common continuation. But white has tried
c,
d,
e and
f.
$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . b 4 . . . . .
$$ | . . 1 X . . 2 . .
$$ | . . . 3 . e . . .
$$ | . a . O . c . f .
$$ | . . d . . . . . .
$$ | . . B . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$W
$$ ------------------
$$ | . . . . . . . . .
$$ | . . b 4 . . . . .
$$ | . . 1 X . . 2 . .
$$ | . . . 3 . e . . .
$$ | . a . O . c . f .
$$ | . . d . . . . . .
$$ | . . B . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
My question is really vague: what's going on here? Why/when does Black make this choice, and what is he hoping to accomplish?