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Simulation and thus scientific computing is the third pillar alongside theory and experiment in todays science and engineering. The term e-science evolved as a new research field that focuses on collaboration in key areas of science using next generation infrastructures to extend the powers of scientific computing. This paper contributes to the field of e-science as a study of how scientists actually work within currently existing Grid and e-science infrastructures. Alongside numerous different scientific applications, we identified several common approaches with similar characteristics in different domains. These approaches are described together with a classification on how to perform e-science in next generation infrastructures. The paper is thus a survey paper which provides an overview of the e-science research domain.