The theory of the elastic scattering of polarized neutrons by magnetic crystals with ordered spins is developed. Several terms which were omitted by Halpern and Johnson in their original treatment of the subject are discussed. These terms vanish in the case of scattering from simple ferromagnetic or antiferromagnetic structures, but they give rise to some interesting effects in more complex structures. Among these is a polarization effect which occurs in antiferromagnetic spirals, proposed recently by Overhauser, Nagamiya, and Izyumov, and an effect which allows the determination of the imaginary part of the form factor in noncentrosymmetric systems. General formulas for the cross section and for the polarization of the scattered beam are given for arbitrary spin orderings.