This paper presents a comprehensive review of advanced control methods specifically designed for floating offshore wind turbines (FOWTs) above the rated wind speed. Focusing on primary control objectives, including power regulation at rated values, platform pitch mitigation, and structural load reduction, this paper begins by outlining the requirements and challenges inherent in FOWT control systems. It delves into the fundamental aspects of the FOWT system control framework, thereby highlighting challenges, control objectives, and conventional methods derived from bottom-fixed wind turbines. Our review then categorizes advanced control methods above the rated wind speed into three distinct approaches: model-based control, data-driven model-based control, and data-driven model-free control. Each approach is examined in terms of its specific strengths and weaknesses in practical application. The insights provided in this review contribute to a deeper understanding of the dynamic landscape of control strategies for FOWTs, thus offering guidance for researchers and practitioners in the field.