Thyroid cancer is the most common cancer of the endocrine system, and, in recent years, there has been a phenomenon of overdiagnosis followed by subsequent overtreatment. This results in an increasing number of thyroidectomy complications being faced in clinical practice. In this paper, we present the current state of knowledge and the latest findings in the fields of modern surgical techniques, thermal ablation, the identification and assessment of parathyroid function, recurrent laryngeal nerve monitoring and treatment and perioperative bleeding. We reviewed 485 papers, from which we selected 125 papers that are the most relevant. The main merit of this article is its comprehensive view of the subject under discussion—both general, concerning the selection of the appropriate method of surgery, and particular, concerning the selection of the appropriate method of prevention or treatment of selected perioperative complications.