Craig developed experimental and theoretical methods for the interpretation of the spectra of molecular crystals which are now the bases of widely used procedures. He worked out the theory of second-order crystalline interactions in molecular crystals and made the first quantitative calculations of exciton energies in a molecular crystal. In valence theory he demonstrated the importance of configuration interaction for π-electrons in aromatic molecules. His early papers on this subject and one written in collaboration with R.G. Parr and I.G. Ross have become standard references in the field. He has also contributed to knowledge of aromatic character, especially in cyclic inorganic systems such as phosphonitrilic halides.