This work presents a systematic review concerning recent studies and technologies of machine learning for Barrett's esophagus (BE) diagnosis and treatment. The use of artificial intelligence is a brand new and promising way to evaluate such disease. We compile some works published at some well-established databases, such as Science Direct, IEEEXplore, PubMed, Plos One, Multidisciplinary Digital Publishing Institute (MDPI), Association for Computing Machinery (ACM), Springer, and Hindawi Publishing Corporation. Each selected work has been analyzed to present its objective, methodology, and results. The BE progression to dysplasia or adenocarcinoma shows a complex pattern to be detected during endoscopic surveillance. Therefore, it is valuable to assist its diagnosis and automatic identification using computer analysis. The evaluation of the BE dysplasia can be performed through manual or automated segmentation through machine learning techniques. Finally, in this survey, we reviewed recent studies focused on the automatic detection of the neoplastic region for classification purposes using machine learning methods.