Efficiency is a critical consideration in the design of hydro turbines. The crossflow turbine is the cheapest and easiest hydro turbine to manufacture and so is commonly used in remote power systems for developing countries. A longstanding problem for practical crossflow turbines is their lower maximum efficiency compared to their more advanced counterparts, such as Pelton and Francis turbines. This paper reviews the experimental and computational studies relevant to the design of high efficiency crossflow turbines. We concentrate on the studies that have contributed to designs with efficiencies in the range of 88-90%. Many recent studies have been conducted on turbines of low maximum efficiency, which we believe is due to misunderstanding of design principles for achieving high efficiencies. We synthesize the key results of experimental and computational fluid dynamics studies to highlight the key fundamental design principles for achieving efficiencies of about 90%, as well as future research and development areas to further improve the maximum efficiency. The main finding of this review is that the total conversion of head into kinetic energy in the nozzle and the matching of nozzle and runner designs are the two main design requirements for the design of high efficiency turbines.