The traditional way of predicting through-space NMR shielding utilizes the McConnell equation which results in the familiar "shielding cones" found in most NMR texts. Ab initio calculations have shown that through-space NMR shielding effects are more complex than that equation, which simply projects through space the anisotropy of the magnetic susceptibility of the functional group ostensibly causing the shielding. In fact, our calculations have shown that in some instances almost half of the (de)shielding effect arises from orbitals associated with the atom experiencing the shielding effect. The net shielding experienced by an atom is a composite of through-space magnetic anisotropy effects, bond or orbital polarization effects and other consequences of the orbital interactions that take place. Our research over the past ten years has shown that Hartree-Fock calculations of through-space NMR shielding values using the GIAO method and a moderate sized basis set give results for through-space shielding that agree well with experimental chemical shift measurements in a variety of systems incorporating various functional groups. Our method will be described and results for the through-space shielding near several common organic functional groups will be discussed. Our computed shielding surfaces will be contrasted with the prediction based on the traditional McConnell shielding cone equation.