The usage of techniques of the artificial neural networks (ANNs) in the field of microwave devices has recently increased. The advantages of ANNs in comparison with traditional full-wave methods are that the prediction speed when the traditional time-consuming iterative calculations are not required and also the complex mathematical model of the microwave device is no longer needed. Therefore, the design of microwave device could be repeated many times in real time. However, methods of artificial neural networks still lag behind traditional full-wave methods in terms of accuracy. The prediction accuracy depends on the structure of the selected neural network and also on the obtained dataset for the training of the network. Therefore, the paper presents a systematic review of the implementation of ANNs in the field of the design and analysis of microwave devices. The guidelines for the systematic literature review and the systematic mapping research procedure, as well as the Preferred Report Items for Systematic Reviews and Meta-Analysis statements (PRISMA) are used to conduct literature search and report the results. The goal of the paper is to summarize the application areas of usage of ANNs in the field of microwave devices, the type and structure of the used artificial neural networks, the type and size of the dataset, the interpolation and the augmentation of the training dataset, the training algorithm and training errors and also to discuss the future perspectives of the usage of ANNs in the field of microwave devices.