Protein kinases play critical roles in cell survival, proliferation, and motility. Their dysregulation is therefore a common feature in the pathogenesis of a number of solid tumors, including thyroid cancers. Inhibiting activated protein kinases has revolutionized thyroid cancer therapy, offering a promising strategy in treating tumors refractory to radioactive iodine treatment or cytotoxic chemotherapies. However, despite satisfactory early responses, these drugs are not curative and most patients inevitably progress due to drug resistance. This review summarizes up-to-date knowledge on various mechanisms that thyroid cancer cells develop to bypass protein kinase inhibition and outlines strategies that are being explored to overcome drug resistance. Understanding how cancer cells respond to drugs and identifying novel molecular targets for therapy still represents a major challenge for the treatment of these patients.