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Crossbreeding results between tropical breeds and European beef breeds as well as within breed (mainly Zebu) genetic variability for some economically important traits is reviewed. Heterosis of between 9% to 11% has been reported for preweaning growth rate, 2% to 11% for postweaning and carcass traits as well as up to 15% for reproduction related traits in crosses involving Bos indicus and Bos taurus cattle. Maximum heterosis was observed in crosses involving Zebu and Criollo cattle, both well adapted to the tropics. Within breed genetic parameter estimates under tropical conditions are still scanty. Based on the production environment and after a review of the literature possible research opportunities and challenged in animal breeding and genetics related to the tropics are discussed.