We propose a new class of representations that can be used for modeling (and model checking) temporal, strategic and epistemic properties of agents and their teams. Our representations borrow the main ideas from interpreted systems of Halpern, Fagin et al.; however, they are also modular and compact in the way concurrent programs are. We also mention preliminary results on model checking alternating-time temporal logic for this natural class of models. Categories and Subject Descriptors I.2.11 [Artificial Intelligence]: Distributed Artificial Intelligence— Multiagent Systems; I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods—Modal logic General Terms Theory Keywords open computational systems, temporal and strategic logics, modeling methodology, model checking