One of the significant objectives of artificial intelligence is to design learning algorithms that are executed on general-purpose computational machines inspired by the human brain. Neural Turing Machine (NTM) is a step towards realizing such a computational machine. In the literature, a variety of approaches have been presented for the NTM; however, there is no existing comprehensive survey and taxonomy for NTM methods. This article presents an overview of taxonomies characterizing the critical concepts of the NTM through a comprehensive survey on the related research activities. This in-depth analysis of taxonomies can provide researchers, designers, and application developers with a clear guideline to compare NTM methods. The taxonomy of machine learning, neural networks, and the Turing machine is introduced. The NTM is also inspected in terms of concepts, structure, implemented tasks, and related works. The article further presents research discussions and future challenges in this area.