With the widespread application of data mining technologies to real life problems, there has been an increasing realization that real data are usually multi-relational, capturing a variety of relations among objects in the same or different entities. For example, in movie recommender systems, the movie rating matrix captures the relation between movies and users, the social network captures the relation among users, and the cast of the movies captures the relation between movies and actors/actresses. The multi-relational data analysis on such data includes two important tasks: (1) To discover multi-relational clusters across multiple entities, i.e., multi-relational clustering. (2) To predict missing entries, i.e., multi-relational missing value prediction. Clustering and missing value prediction give us a better understanding of data and help us with decision making. For example, clusters of users and movies, as well as whether each user cluster likes each movie cluster, provide us with a high-level overview of movie rating data. In addition, the prediction of the missing ratings helps us decide whether to recommend the movies to corresponding users. Moreover, it is particularly meaningful to perform clustering and missing value prediction under the multi-relational setting, since they are able to combine multiple sources of information together effectively, which usually outperforms the algorithms on a single source of data alone. We develop probabilistic models for multi-relational data analysis due to their advantage in incorporating prior knowledge from multiple sources through prior distributions, and their modularity in combining multiple models through sharing latent variables. By performing experiments on a variety of data sets, such as movie recommendation data and ecological data on plant's traits, we show that multi-relational clustering and missing value prediction have superior performance compared to the algorithms on a single data source only.