In eukaryotes, developmental processes and cell differentiation, as well as basic cellular functions require the propagation of information in an asymmetric manner. Localization of mRNA is a key mechanism to establish asymmetric cell fate. The first part of this review provides an overview of our current knowledge of motor protein-dependent mRNA transport in eukaryotes. The second part provides a more detailed description of the most comprehensively studied mRNA translocation complex to date: the ASH1 messenger ribonucleoprotein particle (mRNP) from Saccharomyces cerevisiae. During budding of yeast, the ASH1 mRNP transports cell fate determinants exclusively into the daughter cell. The core factors of the ASH1 mRNP have been identified, their interactions have been studied in detail, and the three-dimensional structure of its mRNA-binding protein, She2p, has been determined. Because no other mRNP has been studied in such detail, the ASH1 mRNP could serve as a model for asymmetric segregation of cell fate determinants in higher eukaryotes.