The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but not limited to computer science, medicine, economics, and industrial applications. Given the continous advancements in deep learning methodologies, there has been a notable surge in its utilization for the estimation of causal effects using counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective functions to estimate counterfactual data unbiasedly. Different from the existing surveys on causal models in machine learning, this review mainly focuses on the overview of the deep causal models based on neural networks, and its core contributions are as follows: 1) we cast insight on a comprehensive overview of deep causal models from both timeline of development and method classification perspectives; 2) we outline some typical applications of causal effect estimation to industry; 3) we also endeavor to present a detailed categorization and analysis on relevant datasets, source codes and experiments.