This thesis describes the synthesis and applications of chemically modified oligonucleotides, principally those containing modifications at the 2´-position of ribose. One application is their use in triplex-forming oligonucleotides (TFOs). DNA triplexes are formed by the binding of a TFO to a DNA duplex. TFOs are potential therapeutic agents against cancer and viral infections. TFOs containing 2´-aminoethoxy-T and 5-MeC were shown by UV melting studies to strongly stabilise parallel triplexes, and by incubation in serum to confer resistance to enzymatic degradation. Therefore these sugar modifications have the potential to improve the biological activity of TFOs. 2´-Modified nucleosides were also used to produce fluorogenic HyBeacon probes by labelling of oligonucleotides containing 2´-aminoethoxy and 2´-azide modified thymidine monomers with NHS esters and alkyne derivatives of fluorescent dyes. The resultant HyBeacons were shown to be effective as genetic probes. The copper catalysed alkyne-azide 1,3-dipolar cycloaddition reaction (the best example of click chemistry) has been used in the nucleic acid field for various applications. However, Cu (I) is cytotoxic so this chemistry is not suitable for use in vivo. The ring strain-promoted azide-alkyne cycloaddition reaction (SPAAC) between a cyclooctyne derivative and an azide does not require metal catalysis. Various modified cyclooctyne active esters and phosphoramidite monomers were synthesised for incorporation into oligonucleotides. Templated DNA strand ligation and crosslinking by the SPAAC reaction were achieved with very fast reaction times. This methodology was used to join oligonucleotides containing several cyclooctynes to complementary azide/fluorophorelabelled oligonucleotides to give covalently fixed fluorescent nanoconstructs. Orthogonal labelling was also achieved by simultaneously reacting oligonucleotides containing multiple cyclooctyne and amino groups with azide and NHS ester derivatives of fluorescent dyes to produce functional HyBeacon probes.