Many modern datasets are naturally expressed in the form of tensors, such as images or videos. Due to their large size and complex structures, separating the information content (signal) from the large amount of non-information (noise) in the data is an especially critical step of the analysis of tensor data. This procedure is known as dimension reduction and the aim of this research is to develop new efficient methods of dimension reduction for tensor data. The developed methods allow both the separation of the data into latent sources and the identification of the signals among them. The different methods are compared theoretically and with both simulations and real data, with a focus on medical imaging data, and are implemented as open source software packages.