The preference of large protein ion channels for cations or anions is mainly determined by the electrostatic interactions of mobile ions with charged residues of the protein. Here we discuss the widely spread paradigm that the charges determining the channel selectivity are only those that can be considered solvent-accessible because of their location near the permeation pathways of ions and water molecules. Theoretical predictions for the electric potential and average ion densities inside the pore are presented using several approaches of increasing resolution: from analytical and numerical solutions of electrostatic equations in a model channel up to all-atom molecular dynamics simulations and continuum electrostatic calculations performed in a particular biological channel, the bacterial porin OmpF. The results highlight the role of protein dieletric properties and the importance of the initial choice of the residue ionization states in the understanding of the molecular basis of large channel selectivity irrespective of the level of resolution of the computational approach used.