Kernel estimation was originally developed to obtain a smooth estimate of a univariate or multivariate probability density from an observed sample of observations. In the spatial case, kernel smoothing creates a smooth map of density values in which the density at each location reflects the concentration of points in the surrounding area. Under kernel estimation, crime "hot spots" appear as irregularly shaped areas of high crime density, areas that can be analyzed in their own right to target crime prevention efforts and assess change over time in crime activity. Once "hot spot" areas are defined, charts and graphs can be prepared to display the characteristics of crimes located within each "hot spot" area, including the number of crimes, their locations, and the dates and times of their occurrence. Another strength of kernel estimation is its usefulness in analyzing change over time. Despite these advantages, using kernel estimation for crime mapping in a law enforcement setting presents many challenges. The technical challenges to implementation and an understanding of how people interact with complex spatial statistical methods in a law enforcement setting are important topics for future research. 15 references