Implicit (level set) representations of shape are known to have several advantages over explicit ones. In particular they do not rely on a specific choice of parameterization and they naturally allow for topological changes of the embedded shapes. In my presentation, I will summarize some recent advances regarding metrics on implicit representations, nonparametric and dynamical shape models for implicit representations, and statistical inference of shapes within a Bayesian framework for segmentation and tracking. These allow, for example, to infer temporally consistent segmentations of an image sequence by computing the most likely embedding function given an input image, and given the embedding functions computed for the previous images.