Mapping applications onto parallel platforms is a challenging problem, that becomes even more difficult when platforms are heterogeneous --nowadays a standard assumption. A high-level approach to parallel programming not only eases the application developer's task, but it also provides additional information which can help realize an efficient mapping of the application. In this paper, we discuss the mapping of pipeline skeletons onto different types of platforms: fully homogeneous platforms with identical processors and interconnection links; communication homogeneous platforms, with identical links but different speed processors; and finally, heterogeneous platforms. We assume that a pipeline stage must be mapped on a single processor, and we establish new theoretical complexity results for two different mapping policies: a mapping can be either one-to-one (a processor is assigned at most one stage), or interval-based (a processor is assigned an interval of consecutive stages). We provide several efficient polynomial heuristics for the most important policy/platform combination, namely interval-based mappings on communication homogeneous platforms.