Two trends apparent in the development of the deep-level transient-spectroscopy (DLTS) method are discussed. The advantages and shortcomings of analysis of the information obtained either by instruments or by mathematical calculations are considered for various distributions of the specific volume. A comparative analysis is made of the methods used widely to process the DLTS curves. The possibility of using the method of mathematical modeling in processing the DLTS curves is considered. A number of recommendations on the use of this method is made and its main advantages are listed. In processing by the mathematical modeling method it is sufficient to record the spectrum using one ''emission window.'' This can be done in any part of the spectrum, including that inside the maximum of a peak. This method can be applied to any correlation function. It can be used to analyze overlapping peaks, to calculate the parameters of deep centers with a high degree of precision, and to obtain additional information from the shape of the spectrum, for example, to find the temperature dependence of the capture cross section of charge carriers at deep centers.