The development of the electron theory of metals is briefly reviewed, and the electronic structures of a selection of monovalent and polyvalent metals are surveyed. Sodium and copper are discussed in detail as examples of the alkali metals and the group IB metals respectively. Agreement between experimental and theoretical values of the binding energies, the lattice constants, the compressibilities and the elastic constants is adequate, but difficulties arise in connection with the calculation of the electronic interactions. These difficulties are increased when divalent metals are considered; the divalent metals calcium, magnesium and beryllium are discussed in this connection. The electronic structures of these metals involve overlap of electrons from the first Brillouin zone, and for magnesium alloys, lattice spacing relationships may be satisfactorily interpreted on this basis. For trivalent aluminium, the mathematical difficulties are more serious; it has, however, been possible to explain the elastic anisotropy of this metal, and the calculated variation of elastic constants with electron/atom ratio enables phenomena encountered in aluminium-rich alloys to be interpreted. The nature of transitional metals is discussed in detail. The possibility of the extension of the theory to alloys is reviewed, with reference to alloys based on copper and on nickel.