Thyroid cancer (TC), due to its heterogeneous nature, remains a clinical challenge. Many factors can initiate the carcinogenesis process of various types of TC, which complicates diagnosis and treatment. The presented review gathers current information on specific types of TC, taking into account the effects of the COVID-19 pandemic. It is likely that COVID-19 has influenced and continues to influence the function of the thyroid gland. A high percentage of patients with COVID-19 showing simultaneous pathological changes in the thyroid suggests that SARS-CoV-2 may disrupt the function of this gland and initiate pro-oxidative mechanisms, inflammatory states, and autoimmune diseases, thereby promoting the formation of neoplastic changes. Furthermore, changes in the expression of the ACE2, TMPRSS2, CLEC4M and DPP4 genes, observed in TC, also occur in COVID-19. Therefore, it is probable that the interaction of SARS-CoV-2 with thyroid cell receptors may initiate carcinogenesis in this gland. Additionally, some drugs used in TC therapy (e.g., levothyroxine) may increase the affinity of SARS-CoV-2 for cells, which could contribute to a more severe course of COVID-19 and the emergence of long-term symptoms (post-COVID-19). Moreover, the consequences of sanitary restrictions (limited access to medical services, reduction in endocrinological and oncological procedures) that took place in many countries during the COVID-19 pandemic may lead in the future to an increased number of missed diagnoses and the emergence of aggressive cancers.