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The continuing transition to renewable energy will require more wind turbines to be installed and operated on land and offshore. On land, wind turbines will increasingly be deployed in hilly or mountainous regions, which are often described together as "complex terrain" in the wind energy industry. These areas can experience complex flows that are hard to model, as well as cold climate conditions that lead to instrument and blade icing and can further impact wind turbine operation. This paper -- a collaboration between several International Energy Agency (IEA) Wind Tasks and research groups based in mountainous countries -- sets out the research and development needed to improve the financial competitiveness and ease of integration of wind energy in hilly or mountainous regions. The focus of the paper is on the interaction between the atmosphere, terrain, land cover, and wind turbines, during all stages of a project life cycle. The key needs include collaborative research and development facilities, improved wind and weather models that can cope with mountainous terrain, frameworks for sharing data, and a common, quantitative definition of site complexity. Addressing these needs will be essential for the affordable and reliable large-scale deployment of wind energy in many countries across the globe. Because of the widespread nature of complex flow and icing conditions, addressing these challenges will have positive impacts on the risk and cost of energy from wind energy globally. [ABSTRACT FROM AUTHOR]