  The existence of one-way functions is arguably the most important problem in
computer theory. The article discusses and refines a number of concepts
relevant to this problem. For instance, it gives the first combinatorial
complete owf, i.e., a function which is one-way if any function is. There are
surprisingly many subtleties in basic definitions. Some of these subtleties are
discussed or hinted at in the literature and some are overlooked. Here, a
unified approach is attempted.
