Change-point, or step-trend, detection is an active area of research in statistics and an area of great interest in hydrology because change points may be evidence of natural or anthropogenic changes in climatic, hydrologic, or landscape processes. A common change-point technique is the Pettitt test; however, many change-point methods are now available and testing of methods has been limited. This study investigated eight methods for detecting change points in the location (central tendency, seven methods) and scale (dispersion or spread, one method) of annual peak streamflows, using simulated data with and without change points, and peak-streamflow series from basins with known large additions of reservoir storage. Parametric methods tested, including a Bayesian one, did not perform well, even when transforming peak streamflows to approximate normality by using logarithms. Nonparametric methods other than the Pettitt test allow for more than one change point but have an unacceptable number of false positives. Based on the results of our methods comparisons, we used the Pettitt and the Mood tests to find change points in location and scale, respectively, in thousands of streamgage records in the conterminous United States. Change points in location (median) and scale are abundant, with the changes in median peak streamflow showing regional patterns, as well as a strong increased streamflow signal around 1970. The changes in scale of peak streamflows are dominated more by temporal than spatial patterns; more streamgages had decreases in scale in earlier decades than recent decades and more streamgages had increases in scale occurring in recent decades than earlier decades.