Since the origin of chronic hemodialysis, a way to quantify the therapy and define its adequacy has been sought. Currently accepted methods rely on the mathematical description of urea kinetics and the evaluation of an index, Kt/V. The history of this concept, and its validation by the National Cooperative Dialysis Study are described. There are six major methods of calculating Kt/V--"three-point" kinetic modeling, "2-BUN" kinetic modeling, percent reduction of urea, In(post/pre-ratio), empirical estimation, and direct quantification of dialysate urea. The assumptions underlying all of these methods are similar: (1) Urea is a valid marker solute for uremic toxicity; (2) urea behaves as described by the mathematical model; (3) input variables can be measured accurately; (4) outputs from the model are consistent and reproducible; and (5) the clinical significance of Kt/V is established by valid outcome studies. Each of these assumptions is examined in turn, and found to be flawed. In particular, the measurement of dialyzer urea clearance is highly method-dependent and inaccurate; measurements in 101 dialyses by four common methods had an overall 27.5% variation among the results of the various methods. Outputs from the six methods of urea monitoring showed wide variation, especially in values of urea distribution volume and protein catabolic rate. Kt/V results were more reproducible, but the clinical significance of a particular value of Kt/V is very poorly established. Urea kinetic modeling is a remarkable conceptual advance and useful tool for understanding the physiology and quantification of dialysis, but Kt/V cannot be a standard for adequacy, since it is both approximate and unvalidated.