We present evidence that the use of orbital based analyses provides an important fundamental basis for interpreting and understanding the significance of features in core-level spectroscopies, in particular, X-ray photoelectron spectroscopy, XPS. A recent paper by Truhlar and colleagues cautions about the limitations of orbital based interpretations of photoelectron spectroscopy for the accurate modeling of the electronic structure of the ions. We provide an alternate view that does use orbitals to derive detailed information from XPS. We discuss the appropriate meaning of Koopmans' theorem as a way to separate the chemically interesting initial state contributions to XPS binding energies, BEs, from the less interesting properties of highly excited ionic states, rather than as a way to estimate values of BEs and BE shifts. The use of orbitals and orbital occupations to take into account the spin and orbital angular momentum coupling that leads to the observed XPS multiplets is shown to be important to understand the number and energy spread of XPS features. The use of a standard approximation to determine the XPS intensities, essential for the theoretical prediction of XPS spectra, is shown to depend on the concept of ionization of electrons from specific orbitals. Finally, the use of orbital properties to identify and include the main many electron correlation of the ionic states in XPS is described. The importance of these considerations is shown by describing examples where they are used in the theoretical determination and the theoretical analysis of the XPS of representative systems. Graphic The orbital description of XPS is shown schematically below for the Ne atom. An orbital description can be applied to and is appropriate to understand the photoemission of complex systems.