The overarching theme of this thesis is the application of aryl boronic esters to the fields of PET and SPECT radiochemistry. Chapter 1 provides an introduction to positron emission tomography (PET) and single photon emission computed tomography (SPECT), in conjunction with an introduction to the utility of arylboranes as precursors for radioisotope incorporation. In chapter 2, a general method for the copper-mediated nucleophilic ¹²³I-iodination of (hetero)aryl boronic pinacol esters and acids is disclosed. This methodology was applied toward the successful radiosynthesis of four commonly used SPECT radiotracers, [¹²³I]DPA- 713, [¹²³I]IMPY, [¹²³I]MIBG and [¹²³I]IPEB. In chapter 3, the copper-mediated nucleophilic ¹⁸F-fluorination of aryl boronic pinacol esters, developed in the Gouverneur group, has been applied to the field of prosthetic group ¹⁸F-radiochemistry. This protocol was utilised to synthesise four popular prosthetic groups in a single radiosynthetic step. Chapter 4 describes the radiosynthesis and biological evaluation of [¹⁸F]DPA-713 and [¹⁸F]CF₃DPA-713, two novel analogues of the Translocator Protein (TSPO) ligand N,N-diethyl-2-(4-methoxyphenyl)-5,7-dimethylpyrazolo[1,5-a]pyrimidine-3- acetamide-713 (DPA-713). Finally, chapter 5 details experimental procedures and characterisation for all compounds.