The formation energy, nature of bonding, electron density of states, and magnetic properties of Fe1-xAlx intermetallics have been calculated in the concentration range 0less than or equal toxless than or equal to0.5 using the tight-binding linearized muffin-tin orbital method and a super unit cell containing 16 atoms. The various concentration ranges are simulated by successively replacing Fe atoms by Al atoms and studying the electronic structure within the density-functional theory and generalized gradient approximation for exchange and correlation. The stability of the Fe1-xAlx alloys increases monotonically with increasing Al concentration, while the magnetic moment variation reveals exactly the opposite behavior. Stoichiometric FeAl is found to exhibit two nearly degenerate magnetic structures: a nonmagnetic state with zero moment on Fe and a ferromagnetic state with a moment of 0.75mu(B) per Fe atom. Fe3Al, on the other hand, is ferromagnetic with a calculated moment of 2.45mu(B) at the Fe-I site and 1.95mu(B) at the Fe-II site. The coupling between Fe and Al atoms is antiferromagnetic, although the moment at the Al site is much smaller (-0.17mu(B)) than that at the Fe sites. The bonding between Fe and Al atoms is primarily due to the hybridization between the 3d electrons of the former and the sp electrons of the latter. The bonding has a strong local character in that the coupling is between the nearest neighbor atoms. This is further verified by a calculation using small clusters as models of the bulk structure. The density of states at the Fermi energy is dominated by contributions from the Fe 3d state although its variation with Al is modulated by subtle interaction with Al 3p electrons. The total densities of states at the Fermi energy of Fe1-xAlx alloys show the same variation as the electrical resistivity, suggesting that the increase and then decrease in resistivity with Al concentration with a peak at 33% Al is purely of electronic origin.