Positron Emission Tomography (PET) is emerging as a powerful method for imaging cancer through the design and development of new radiotracers. Antibodies have promising properties as ligands for targeting cancer, as they have the advantage of displaying high affinity for their respective receptors. However, the use of antibodies as radiotracers is limited to the use of long-lived isotopes, as these large biomolecules additionally display slow blood circulation and clearance. The use of short-lived isotopes such as 18F or 68Ga, in combination with antibodies, would provide the ideal balance between targetability and clearance. This may be achieved by use of a two-step pretargeting strategy, whereby a reactive tag is conjugated to the antibody and allowed to localise in the tissue to be imaged, before systemic administration of a chemical reporter (e.g. a labelled reactive partner) which allows the ‘pretargeted’ tissue to be imaged. The Strain-Promoted Azide/Alkyne Cycloaddition (SPAAC) reaction between cyclooctynes and azides was evaluated as an appropriate bioorthogonal reaction for application to a pretargeting strategy using short-lived isotopes. The synthesis of a library of cyclooctyne precursors was carried out, which were evaluated in terms of their reactivity with azides, and their suitability for in vivo applications. An 18F-labelled version of the SPAAC reaction was developed, demonstrating the ability of the reaction to be carried out under different conditions. This model reaction was translated to in vivo pretargeting using a cyclooctyne modified Herceptin monoclonal antibody and an 18F-labelled azide. These initial experiments indicated that the SPAAC reaction may not be fast enough to occur at the low concentrations which are found in vivo. The reaction was thoroughly examined in terms of kinetics at different concentrations, and a high concentration-dependence upon rate of reaction was confirmed. This was supported by a 68Ga-labelled SPAAC reaction, which was carried out using reportedly more reactive cyclooctynes than those used in the initial experiments. In general, the reaction showed a greater preference to be carried out in organic solvents such as acetonitrile, and under closer to physiological conditions the reactions were less likely to proceed. The Inverse-electron-Demand Diels-Alder (IeDDA) reaction between tetrazines and strained alkenes was evaluated as an alternative bioorthogonal reaction for demonstrating in vivo pretargeting. A series of 68Ga-labelled IeDDA reactions between a 68Ga-labelled tetrazine and a series of norbornene analogues demonstrated the superior reaction kinetics and biocompatibility of the IeDDA reaction. The initial translation of the IeDDA reaction to a proof-of-concept for pretargeting using cyclic RGD pentapeptides was initially unsuccessful, attributed to the surprisingly poor reactivity of norbornene-modified cyclic RGD pentapeptides towards a 68Ga-labelled tetrazine. The reaction between a 68Ga-labelled tetrazine and a Cetuximab antibody, which had been modified with the more reactive trans-cyclooctene (TCO) moeity, was successfully demonstrated. The hypothesised pretargeting strategy using this model reaction was achieved on high EGFR expressing cells, validating the IeDDA reaction in this context. These results suggested tantalising opportunities for application of the IeDDA reaction to in vivo pretargeting for PET imaging using short-lived isotopes such as 18F and 68Ga.