Bayes filters recursively estimate the state of dynamical systems from streams of sensor data. Key components of each Bayes filter are probabilistic prediction and observation models. In robotics, these models are typically based on parametric descriptions of the physical process generating the data. In this talk I will show how non-parametric Gaussian process prediction and observation models can be integrated into different versions of Bayes filters, namely particle filters and extended and unscented Kalman filters. The resulting GP-BayesFilters can have several advantages over standard filters. Most importantly, GP-BayesFilters do not require an accurate, parametric model of the system. Given enough training data, they enable improved tracking accuracy compared to parametric models, and they degrade gracefully with increased model uncertainty. We extend Gaussian Process Latent Variable Models to train GP-BayesFilters from partially or fully unlabeled training data. The techniques are evaluated in the context of visual tracking of a micro blimp and IMU-based tracking of a slotcar.