There has been considerable controversy during the past few years concerning the validity of the classical log law that describes the overlap region of the mean-velocity profile in the canonical turbulent boundary layer. Alternative power laws have been proposed by Barenblatt, Chorin, George, and Castillo, to name just a few. Advocates of either law typically have used selected data sets to foster their claims. The experimental and direct numerical simulation data sets from six independent groups are analyzed. For the range of momentum-thickness Reynolds numbers of 5£ 10 2 ‐2:732£ 10 4 , the best-fit values are determined for the “constants” appearing in either law. Our strategy involves calculating the fractional difference between the measured/computed mean velocity and that calculated using either of the two respective laws. This fractional difference is bracketed in the region § §0:5%, so that an accurate, objective measure of the boundary and extent of either law is determined. It is found that, although the extent of the power-law region in outer variables is nearly constant over a wide range of Reynolds numbers, the log-region extent increases monotonically with Reynolds number. The log law and the power law do not cover the same portion of the velocity profile. A very small zone directly above the buffer layer is not represented by the power law. On the other hand, the inner region of the wake zone is covered by it. In the region where both laws show comparable fractional differences, the mean and variance were calculated. From both measures, it is concluded that the examined data do not indicate any statistically significant preference toward either law. I. The Opening Arguments T HE Reynolds numbers encountered in many practical situations are typically several orders of magnitude higher than those studied computationally or even experimentally. High-Reynoldsnumber research facilities are expensive to build and operate, and the few existing are heavily scheduled with mostly developmental work. For traditional wind tunnels, additional complications are introduced at high speeds due to compressibility effects and probe-resolution limitations near walls. Likewise, full computational simulation of high-Reynolds-number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will, therefore, continue to play a vital role in the computation of high Reynolds number practical flows using the Reynolds averaged Navier‐Stokes equations. Because the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed toward the low Reynolds numbers, the key question in modeling high-Reynolds-number flows is what the Reynolds number effects are on the mean and statistical turbulence quantities. One of the fundamental tenets of boundary-layer research is the idea that, for a given geometry, any statistical turbulence quantity (mean, rms, Reynolds stress, etc.) measured at different facilities and at different Reynolds numbers will collapse to a single universal profile when nondimensionalized using the proper length and velocity scales. (Different scales are used near the wall and away from it.) This is termed self-similarity or self-preservation and allows convenient extrapolation from the low-Reynolds-number laboratory experiments to the much higher-Reynolds-number situations encountered in typical field applications. The universal log profile