The aim of this talk is to introduce the Thurston asymmetric metric on Teichmueller space and to explain some of its nice features. This metric is a Finsler metric which is not symmetric, which means that one can find in Teichmueller space two points a,b for which the distance from a to b is not equal to the distance from b to a. Thurston developed a theory for that metric which looks like that of Teichmueller metric, but with its specific features and properties.