<p>A&#xa0;brief review is provided of new approaches to characterizing the surface quality of metalworking products. These approaches are based on mathematical procedures involving a&#xa0;large amount of computation, including fractal methods. An analysis was conducted to compare computational methods for estimating the fractal dimensions of surface roughness microprofiles in steel alloy parts produced using electrical discharge machining. The microprofiles with a&#xa0;given fractal dimension were obtained via a&#xa0;structural and functional method using Brownian motion. The fractal dimension was estimated using two analyzed methods (the spectral method and a&#xa0;method for plotting the area-scale function) and compared with the given value. The accuracy of estimated values was assessed. It is established that the spectral method can be used to estimate the fractal dimension over the entire range of the signal power spectrum; however, the error in determining the fractal dimension will be greater than when the area-scale function method is used. In addition, when estimating the fractal dimension of a&#xa0;surface roughness profile via the spectral method, additional filtering, smoothing, and centering with the use of weight windows are required, which leads to signal truncation. Truncation distorts high-frequency signal components and underestimates the fractal dimension. The fractal dimension estimation of actual surface microprofiles via the area-scale function method was found to be more accurate than its estimation via the spectral method. Therefore, in order to determine the fractal dimension of surface microprofiles, it is recommended to use the area-scale function method. The obtained results can be used in the processing of measurement data in accordance with modern standards in the field of geometric surface characteristics, including the development of software for roughness measuring instruments.</p>