The field of machine translation (MT) has advanced over the years, with three major approaches dominating the field: Rule-Based Machine Translation (RBMT), Statistical Machine Translation (SMT), and Neural Machine Translation (NMT). This research paper provides an extensive review of these approaches, including their development, advantages, and disadvantages. Initially, RBMT represented a cutting-edge technology, performing translation using dictionaries and explicit language rules. However, dealing with intricate linguistic patterns was severely hindered by its rigidity and limited scalability, which gave rise to SMT. In order to provide more flexible translations, SMT used statistical models to extract patterns from large multilingual corpora. This method became well-known since it was data-driven, but it still had problems with domain adaptation and a lack of high-quality parallel data. With the introduction of NMT, a breakthrough occurred in the field of translation. NMT uses deep learning techniques including recurrent neural networks and Transformer-based neural networks to produce more meaningful and accurate information. Since NMT is end-to-end, it increases translation efficiency and has no RBMT or SMT limitations, especially for low-resource languages and complex sentence structures. In this paper, we discuss these approaches used by the numerous researchers in this field, and highlight their respective advantages and disadvantages.