Classical methods for processing and analysis of multidimensional signals – such as color videos and hyperspectral images – do not exploit full information contained in inner their factors. On the other hand, recently developed tensor based methods allow for data representation and analysis which directly account for data multidimensionality. Examples can be found in many applications such as face recognition, image synthesis, video analysis, surveillance systems, sensor networks, data stream analysis, marketing and medical data analysis, to name a few. This talk will be focused on presentation of the basic ideas, as well as recent achievements, in the domain of tensor based signal processing. A systematic overview of tensor data representation, tensor decompositions, as well as pattern recognition with tensors will be presented. Practical aspects and tensor implementation issues will be also discussed.