Two-phase flow regimes have a profound influence on all the two-phase transport processes. Consequently, their correct identification is a task of major importance. Two main components are needed in the identification process: flow regime indicator and classifier. In the first pioneering works, visual flow regime maps were obtained. In this case, the visual information was the flow regime indicator and the researcher judgement was used as flow regime classifier. This approach presents a high level of subjectivity. In the last decades, important work in obtaining more objective flow regime indicators and classifiers has been done. In this review the current knowledge about flow regime indicators and classifiers in thermal-hydraulic applications is summarized. Flow regime indicators comprise different statistical parameters of void fraction and bubble chord length distributions. Flow regime classifiers cover different artificial neural network architectures such as self-organized and probabilistic neural networks. Finally, the main flow regime identification works performed in different flow channel geometries are reported.