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 G-tract 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 G-quadruplex forming aptamers. The perspectives and potential developments of this research area are also discussed.