The 2nd International Workshop on Theory and Practice of Open Computational Systems (TAPOCS 2004) was one of the events of the 13th IEEE International Workshops on Enabling Technologies: Infrastructures for Collaborative Enterprises (WETICE-2004). TAPOCS aims at exploring the various forms of openness for computational systems. We are interested in investigations of models and formal frameworks for open computation, as well as in issues related to the engineering and applications of open computational systems. This report provides an overview of the scientific activity that took place at TAPOCS 2004. After an introduction to the scope and goals of the workshop, presentations are shortly summarized, and organized in a coherent conceptual framework along with the results from discussions. Finally, open issues are reported as well as some considerations about the future of TAPOCS.