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Models for network topology form a crucial component in the analysis of protocols. This paper systematically investigates a variety of evolutionary models for autonomous system (AS) level Internet topology. Evolution-based models produce a topology incrementally, attempting to reflect the growth patterns of the actual topology. While evolutionary models are appealing, they have generally not agreed as closely with measurements of real data as non-evolutionary models. We attempt to understand what factor contributes to a "good" evolutionary model. Our systematic study consists of a relatively generic evolutionary model framework, which we populate with different choices for the components. This allows us to compare a variety of instances of models to measurements from real data sets. We study issues such as the initial topology, the type of preferential connectivity used when adding edges, and the role of "growth" edges added between existing nodes. We find that appropriate instantiation of the framework can provide topologies that agree closely with real data. We also use our work to highlight several crucial open problems in topology modeling.