In this paper, we deal with the problem of scheduling independent tasks on heterogeneous master-slave platforms. We target both o-line and on-line problems , with several objective functions (makespan, maximum response time, total completion time). On the theoretical side, our results are twofold: (i) For o-line scheduling, we prove several optimality results for problems with release dates; (ii) For on-line scheduling , we establish lower bounds on the competitive ratio of any deterministic algorithm. On the practical side, we have implemented several heuristics, some classical and some new ones derived in this paper, on a small but fully heterogeneous MPI platform. Our results show the superiority of those heuristics which fully take into account the relative capacity of the communication links.