Spectral methods have been applied for more than 40 yr to calculate the depth to magnetic sources and the Curie point depth or Moho depth. Unfortunately, conceptual, theoretical and methodological errors, as well as, subjective approaches and lack of rigor in the application of the method are common. This has affected reproducibility, credibility and confidence in this method. We carried out a detailed mathematical and methodological revision of the spectral methods (centroid, spectral peak, forward and fractal methods) applied to magnetic data for the determination of the depth to magnetic sources. Moreover, a systematic analysis of more than 110 articles was done in order to compile and compare the different approaches and values of key parameters used by different authors in their calculations. We discuss difficulties, conditions and methodological procedures, as well as several misapplications and misinterpretation of the different methods.