Linnett proposed his theory 45 years after Lewis's supposition. During these years Pauling, Mulliken and Hund made different molecular structure models based on valance bond and molecular orbital theory. Their theories were seemed to fit many experiences but had some inabilities. Linnett's double quartet theory could solved some important problems about stability of radicals, paramagnetism / diamagnetism in molecular systems, electronic structure in transition states and finally challenge of resonance and aromaticity. In this article we review some basic ideas and concepts concerning different models and then we give a detailed discussion of the LDQ and use it in diverse branches of chemistry.