The diagnosis of thyroid cancer (TC) has increased dramatically in recent years. Papillary TC is the most frequent type and has shown a good prognosis. Conventional treatments for TC are surgery, hormonal therapy, radioactive iodine, chemotherapy, and targeted therapy. However, resistance to treatments is well documented in almost 20% of all cases. Genomic sequencing has provided valuable information to help identify variants that hinder the success of chemotherapy as well as to determine which of those represent potentially druggable targets. There is a plethora of targeted therapies for cancer, most of them directed toward point mutations; however, chromosomal rearrangements that generate fusion genes are becoming relevant in cancer but have been less explored in TC. Therefore, it is relevant to identify new potential inhibitors for genes that are recurrent in the formation of gene fusions. In this review, we focus on describing potentially druggable variants and propose both point variants and fusion genes as targets for drug repositioning in TC.