Physical Properties: hard, ductile, malleable, electrically conductive, thermally conductive, high mp, high bp
What type of bonding leads to this?
Metals are crystalline (i.e., atoms are regularly spaced in three dimensions) but have no ions, so consider covalent bonding in a crystalline lattice built up a little at a time.
In metals the bands are not completely filled; since there are more bonding states filled than antibonding there is a net bond energy that can be quite large - hence high mp and bp The metal molecular orbitals are extended over many atoms (hundreds or thousands).
The energy of the highest occupied molecular orbital in a metal is called the Fermi Level:
Adding heat or electrical energy: the electrons can accommodate additional energy because the empty excited states are at very low energy; further, the input energy can be distributed over the entire lattice because the wavefunctions are delocalized over large numbers of atoms. Thus, metals have high electrical and thermal conductivities.
Why is there any electrical resistance?
Defects in the lattice disrupt the delocalization of wavefunctions. "Defects" can be created by vibrations. Since the number of vibrations that are active depends on temperature, thus the resistivity must also depend on temperature. In general, conductivity = σ = neμ, where n is the number of charge carriers, e is the electronic charge, and μ is the mobility.