The continuous development of electronic systems has made the analog, digital, and mixed-signal circuits more sophisticated, thus posing great difficulties to the existing fault detection and diagnosis (FDD) methods. Traditional methods are mostly non-scalable, cannot be adapted to different situations and cannot even sometimes recognize the same fault among various conditions. The present work is to compare the fault diagnosing performance of various models based on neural networks (NNs) in electronic circuits and to point out the NN architectures, optimizations and hybrid learning techniques that the FDD performance of the NN models. A thorough literature review study was done for 28 papers attesting the use of NNs in the circuit fault diagnosis written between the years 2016 and 2025 published in the scientific journals of IEEE Xplore, Springer, Elsevier, and MDPI. The types of neural network architectures, fault classification accuracy, noise and dynamics robustness, and benefits from optimization and feature extraction methods were the main aspects of the papers under review. The findings show that multi-valued neuron networks, conditional variational NNs, convolutional neural networks, denoising autoencoders, and optimized backpropagation models continuously outperform the traditional methods by acquiring higher accuracy, faster convergence and robust fault detection even in the most complex and demanding real-time environments. In addition, the training process is made easier and fault identification is made wider by optimization and hybrid learning approaches through improved training efficiency and multi-fault classification. Generally, neural network-based FDD offers an intelligent, adaptive, and resilient solution that has the power to revolutionize the development of future electronic systems with the characteristic of being smart and robust.