Core X-ray photoelectron spectroscopic (XPS) data often contain overlapping chemically shifted peaks that differ in their width, peak shape, and intensity. The spectra may be complicated by the presence of satellite and multiplet splitting features as well as from the X-ray satellites that arise when achromatic X-radiation is used. Curve fitting has been extensively used for more than the past 50 years as a means of extracting chemical information from the overlapping features in core XPS. Our understanding of the key components of this approach, such as the fitting function and the spectral background, has improved substantially over the years.XPS is now the most widely used surface analytical method, and many users often have their principal expertise in other areas. While the associated computer software in most XPS instruments has powerful data analysis techniques, including curve fitting, provided by the manufacturer or by a separate commercial source, the application of these techniques may not always be appropriately applied. This perspective article gives the author's view of the main issues that impact the use of curve fitting, together with a description of some approaches that misuse curve fitting leading to erroneous conclusions about the surface chemistry. The article is illustrated by examples showing the fitting of various types of spectra using true Voigt functions.