Microsystems are widely used in 5G, the Internet of Things, smart electronic devices and other fields, and signal integrity (SI) determines their performance. Establishing accurate and fast predictive models and intelligent optimization models for SI in microsystems is extremely essential. Recently, neural networks (NNs) and heuristic optimization algorithms have been widely used to predict the SI performance of microsystems. This paper systematically summarizes the neural network methods applied in the prediction of microsystem SI performance, including artificial neural network (ANN), deep neural network (DNN), recurrent neural network (RNN), convolutional neural network (CNN), etc., as well as intelligent algorithms applied in the optimization of microsystem SI, including genetic algorithm (GA), differential evolution (DE), deep partition tree Bayesian optimization (DPTBO), two stage Bayesian optimization (TSBO), etc., and compares and discusses the characteristics and application fields of the current applied methods. The future development prospects are also predicted. Finally, the article is summarized.