Graphical Abstract Abstract Computational drug repurposing is a screening method for drug discovery that utilizes a wide spectrum of techniques and tools. It reduces the process cost and time of introducing drugs to the market. No need to mention that drug-related subject is a critical field, therefore, makes screening challenging and an important step for further drug investigations. This work tends to study four approaches of computational drug repurposing, i.e., factorization-based methods, machine learning methods, deep learning methods, and graph neural networks. To achieve this aim, we propose new methods for each approach and discuss their performances, challenges, advantages, and disadvantages. To cover the first approach, we propose a novel tensor-matrix-tensor (TMT) formulation as a new data array method with a gradient-based factorization procedure. To cover the second approach, we present two machine learning algorithms, i.e., SVM and random forest, with a new embedding representation. The paper compares the proposed approaches with two deep-learning methods and a graph attention network model on two datasets and discusses their results. The results show deep learning methods outperform other approaches.