This doctoral thesis presents the results of my work into the visualization of high dimensional time-dependent data. Specifically, two new algorithms are presented: Probabilistic Principal Components Through Time, and GTM Through Time. The former is a linear mapping taking time dependence into account, which is a special case of the linear Kalman Filter. The latter is a non-linear mapping technique where a non-linear two-dimensional manifold, discretized as a regular grid of points, is fitted through the data. Each grid point corresponds to a hidden state of a Hidden Markov Model. The model builds on the existing Generative Topographical Mapping (GTM) technique for time-independent data. Both techniques utilize a particular form of probabilistic graphical model, namely a Directed Acyclic Graph, in order to achieve the extension from a time-independent model to the time dependent case. The models are trained by maximizing the log likelihood of the data given the model using the Expectation-Maximization (EM) algorithm. The behaviour of the techniques is demonstrated using toy data, and results are also presented using a real engineering data set, from a human patient monitoring application.