The natural sequences of nucleic acids generally consist of nucleotides linked together by canonical 3'-5' phosphodiester bonds. An inversion of polarity site (IPS) can be defined as the point of the sequence in which a 3'-3' or a 5'-5' phosphodiester bond occurs. By extending this definition, an IPS can be described as that part of the sequence in which two 3'- or two 5'-hydroxyl groups are connected by a linker, variable in size or in chemical nature. In G-quadruplex structures an IPS can be introduced in three different positions: inside a non G-tract, inside a G-tract and just between a non Gtract and a G-tract. Investigations have been reported concerning all the three types of modification. This review describes the effects of the presence of one or more IPSs in G-quadruplex structures, particularly regarding their topological and structural characteristics, glycosidic bond preference, and thermal stability, with special attention to biologically active Gquadruplex forming aptamers. The perspectives and potential developments of this research area are also discussed.