In this article, two new approaches are introduced which describe redox reactions through descriptors defined within the field of conceptual density functional theory (DFT). One approach starts with the grand canonical ensemble DFT from which a formula is derived for the chemical potential of the electrode in terms of intrinsic properties of oxidized and reduced states of the electroactive species. Second, starting from a Born-Haber scheme, the redox potential is solely expressed in terms of the vertical electron affinity and ionization potential of oxidized and reduced species, respectively. A large collection of 44 organic and inorganic systems are studied in different solvents including implicit and explicit solvation models. Both strategies seem well capable of reproducing experimental values of redox potentials.