Recently, several theoretical models of parallel architec- tures have been proposed to replace the PRAM as the model that is presented to an algorithm designer. A primary focus of the new models is to include the cost of interprocessor commu- nication, which is increasingly important in modern parallel architectures. We argue that modeling the communication costs in the architecture or system is only one part of the problem. The other, and usually much more difficult, part is modeling the communication properties of the algorithm itself, which provides necessary inputs into the architectural model to deter- mine overall complexity. In this context, we make three main points in this paper: (i) It is incomplete to describe communica- tion without regard to its relationship with replication. We propose a description of the communication-replication rela- tionship in terms of the working set hierarchy of an algorithm. (ii) Both inherent communication and the communication- replication relationship can be very difficult to model in irreg- ular, dynamic computations that are crucial in many real-world applications. We present some examples that demonstrate this difficulty. (iii) We believe that substantial leverage can be obtained in this effort from the computer systems community, which can provide a hierarchy of simulation and profiling tools-from abstract to detailed-tailored to the needs of the algorithm designers. We propose an initial set of simulation tools, and we discuss possible future refinements to this set.