With the rapid growth of cloud computing, the number of data centers (DCs) continuously increases, leading to a high-energy consumption dilemma. Cooling, apart from IT equipment, represents the largest energy consumption in DCs. Passive design (PD) and active design (AD) are two important approaches in architectural design to reduce energy consumption. However, for DC cooling, few studies have summarized AD, and there are almost no studies on PD. Based on existing international research (2005-2024), this paper summarizes the current state of cooling strategies for DCs. PD encompasses floors, ceilings, and layout and zoning of racks. Additionally, other passive strategies not yet studied in DCs are critically examined. AD includes air, liquid, free, and two-phase cooling. This paper systematically compares the performance of different AD technologies on various KPIs, including energy, economic, and environmental indicators. This paper also explores the application of different cooling design strategies through best-practice examples and presents advanced algorithms for energy management in operational DCs. This study reveals that free cooling is widely employed, with Artificial Neural Networks emerging as the most popular algorithm for managing cooling energy. Finally, this paper suggests four future directions for reducing cooling energy in DCs, with a focus on the development of passive strategies. This paper provides an overview and guide to DC energy-consumption issues, emphasizes the importance of implementing passive and active design strategies to reduce DC cooling energy consumption, and provides directions and references for future energy-efficient DC designs.