For many years, gene alterations of the mitogen activated protein kinase pathway have been investigated in papillary thyroid carcinomas (PTC) and the radiation-specific induction of Ret/PTC rearrangements has been discussed in the published literature. According to recent studies, these alterations are now considered as age-related changes rather than radiation-specific changes in PTC. Thus, there is a strong motivation to search for novel alterations that might represent radiation-specific markers in PTC. DNA copy number alterations (CNAs) are frequent in human cancers and are also prevalent in PTC. However, the only way to tease out radiation-specific CNAs is a comparative analysis of CNAs from closely matched tumour cohorts, as various factors such as the age of patients or the histology of tumours also influence the type and frequency of CNA. Therefore, this review focuses on the current knowledge on CNAs in PTC and on future strategies to identify radiation-specific changes in these tumours.