The existence of one-way functions (owf) 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. I attempt a unified approach.