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We study methods to statically approximate "first-order" process calculi (Pi, Join) by "propositional" models (CCS, BPP, Petri nets). We consider both open and closed behavior of processes. In the case of open behavior, we propose a type system to associate pi-calculus processes with restriction-free CCS types. A process is shown to be in simulation relation with each of its types, hence safety properties that hold of the types also hold of the process. We refine this approach in the case of closed behavior: in this case, types are BPP processes. Sufficient conditions are given under which a minimal BPP type can be computed that is bisimilar to a given process. These results are extended to the Join calculus using place/transition Petri nets as types.