In this paper, we deal with algorithmic issues on heterogeneous platforms. We show that static scheduling and load-balancing strategies are absolutely needed to achieve good performances, in contrast to situation for homogeneous parallel machines where dynamic schemes often turn out to be very satisfactory. However, we also show that static strategies targeted to heterogeneous platforms are difficult to design and implement: intuitively, data distribution must obey a much more refined model than standard block-cyclic distributions to equally balance the load between processors of different speeds. Technically, we state several NP-completeness results that demonstrate the intrinsic difficulty of static load-balancing on heterogeneous platforms.