We initiated this work with in-depth research on key areas related to tensors and their decompositions in the context of computer vision. First, we focused on defining certain matrix multiplications that are necessary when working with tensors and their decompositions. After that, we delved into the definition of tensors and their basic components, such as fibers and tensor slices. Additionally, we defined fundamental tensor operations required for their processing. Finally, in a brief description, we presented Singular Value Decomposition (SVD) as a technique for matrix decomposition. All this theoretical foundation serves as a basis for further research and application of tensor decompositions in computer vision. Next, we described Tucker decomposition, which is a powerful tool for tensor analysis. Tucker decomposition breaks down a tensor into its core and factor matrices for each dimension. This decomposition enables us to understand the structure of tensors and extract significant characteristics. We particularly highlighted HOSVD, a special version of Tucker decomposition that can be considered a generalized version of SVD for multidimensional tensors. Lastly, we presented the Tensor Train decomposition, the most recent decomposition developed to address specific issues of other decompositions. This decomposition provides flexibility and efficiency in handling large-dimensional tensors.