In 1824 Hering introduced an indicator-dilution method for measuring blood velocity. Not until 1897 was the method extended by Stewart to measure blood (volume) flow. For more than two decades, beginning in 1928, Hamilton and colleagues measured blood flow, including cardiac output. They proposed that the first-passsage indicator concentration-time curve could be recovered from observed curves that included recirculation by semilogarithmic extrapolation of the early downslope. Others followed with attempts to fit the complete first-passage curve by various forms, such as by the sum of three exponential terms (three well-stirred compartments in series). Stephenson (1948) thought of looking at indicator-dilution curves as convolutions of indicator input with a probability density function of traversal times through the system. Meier and I reached a similar conclusion, and extended it. The fundamental notion is that there exists a probability density function of transit times, h(t), through the system. We proved that mean transit time t= V/F, where V is volume in which the indicator is distributed. Thus, V, F, and t might all be calculated, or r alone might suffice if one wanted only to know relative blood flow. I extended the analysis to include residue detection of indicator remaining in the system, so that V, F, and could be calculated by external monitoring. Chinard demonstrated the value of simultaneous multiple indicator-dilution curves with various volumes of distribution. Goresky extended the technique to study cell uptake and metabolism. He also found a transform of indicator-dilution output curves (equivalent to multiplying the ordinate by tand dividing the time by t) which made congruent the family of unalike curves obtained by simultaneous injection of indicators with different volumes of distribution. Bassingthwaighte showed the same congruency with the transform of outputs of a single indicator introduced into a system with experimentally varied blood flows. We showed the same congruency for the pulmonary circulation, adding a correction for delays. Success of these transforms suggests that the architecture of the vascular network is a major determinant of the shape of density functions of transit times through the system, and that there is in this architecture, a high degree of self-similarity, implying that the fractal power function is a component in shaping the observed density of transit times. I proposed that the distribution of capillary critical opening pressures, which describes recruitment of vascular paths, may be important in shaping indicator-dilution curves, and that h(t) may be derived from flow-pressure and volume-pressure curves under some circumstances.