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Traditional approaches for simultaneous localization and mapping (SLAM) rely on geometric features such as points, lines, and planes to infer the environment structure. They make hard decisions about the (data) association between observed features and mapped landmarks to update the environment model. This paper makes two contributions to the state of the art in SLAM. First, it generalizes the purely geometric model by introducing semantically meaningful objects, represented as structured models of mid-level part features. Second, instead of making hard, potentially wrong associations between semantic features and objects, it shows that SLAM inference can be performed efficiently with probabilistic data association. The approach not only allows building meaningful maps (containing doors, chairs, cars, etc.) but also offers significant advantages in ambiguous environments.