The focus of the novel research reported in this thesis is the labelling of nucleic acids by catalyst-free 1,3-dipolar cycloaddition reactions. Both nitrile oxide-alkyne cycloadditions (NOAC) and strain-promoted azide-alkyne cycloadditions (SPAAC) were explored. The possiblitity for ‘pre-synthetic’ functionalisation was demonstrated using non-nucleosidic phorphoramidite building blocks generated by NOAC. Three isoxazole phosphoramidites were prepared. Following in situ generation of the nitrile oxides from 1,2-, 1,3- or 1,4-disubstituted hydroxyethoxybenzaldehyde oximes and highly regioselective cycloadditions to a simple alkyne, the isomeric isoxazoles were obtained in excellent yields. Functional group interchange of the pendant hydroxy group to a phosphoramidite functionality facilitated coupling to DNA both by manual and instrument controlled solid phase DNA synthesis. Photoresponsive DNA, incorporating isomeric isoxazole-linked azobenzene moieties, was prepared by ‘post-synthetic’ modification of alkyne-functionalised oligonucleotides by NOAC. The compatibility of the azobenzene functionality with NOAC protocols was first confirmed with small molecule examples; the resulting cycloadducts were characterised by NMR spectroscopy and mass spectrometry (MS). Oligonucleotides incorporating azobenzene moieties at either the 5’- or the 3’- termini, or at an internal position, were subsequently synthesised and the photochemical and kinetic properties of selected examples were determined. A relationship was found between the thermodynamic and photochemical properties of the modified oligonucleotides and the substitution pattern on the aryl rings of the azobenzene moiety. DNA and 2’-OMe RNA sequences conjugated to a variety of chemically and biologically significant ligands were prepared by solid-phase SPAAC. A strained-cyclooctyne phosphoramidite was first conjugated to the 5’-terminus of oligonucleotides. Several azide labels were prepared, including benzyl, cinnamyl, biotinyl, cholesteryl and fluoresceinyl. Conjugation was clean and efficient in all cases. Oligonucleotides were characterised by HPLC and MALDI-TOF MS.