The article presents a multidimensional (MD) approach to recommender systems that can provide recommendations based on additional contextual information besides the typical information on users and items used in most of the current recommender systems. This approach supports multiple dimensions, profiling information, and hierarchical aggregation of recommendations. The article also presents a multidimensional rating estimation method capable of selecting two-dimensional segments of ratings pertinent to the recommendation context and applying standard collaborative filtering or other traditional two-dimensional rating estimation techniques to these segments. A comparison of the multidimensional and two-dimensional rating estimation approaches is made, and the tradeoffs between the two are studied. Moreover, the article introduces a combined rating estimation method, which identifies the situations where the MD approach outperforms the standard two-dimensional approach and uses the MD approach in those situations and the standard two-dimensional approach elsewhere. Finally, the article presents a pilot empirical study of the combined approach, using a multidimensional movie recommender system that was developed for implementing this approach and testing its performance.