Thyroid cancer is a rare malignancy in the pediatric population that is highly associated with disease aggressiveness and advanced disease stages when compared to adult population. The biological and molecular features underlying pediatric and adult thyroid cancer pathogenesis could be responsible for differences in the clinical presentation and prognosis. Despite this, the clinical assessment and treatments used in pediatric thyroid cancer are the same as those implemented for adults and specific personalized target treatments are not used in clinical practice. In this review, we focus on papillary thyroid carcinoma (PTC), which represents 80–90% of all differentiated thyroid carcinomas. PTC has a high rate of gene fusions and mutations, which can influence the histologic subtypes in both children and adults. This review also highlights telomere-related genomic instability and changes in nuclear organization as novel biomarkers for thyroid cancers.