From the perspective of historical review, the methodology of economics develops from qualitative to quantitative, from a small sampling of data to a vast amount of data. Because of the superiority in learning inherent law and representative level, deep learning models assist in realizing intelligent decision-making in economics. After presenting some statistical results of relevant researches, this paper systematically investigates deep learning in economics, including a survey of frequently-used deep learning models in economics, several applications of deep learning models used in economics. Then, some critical reviews of deep learning in economics are provided, including models and applications, why and how to implement deep learning in economics, research gap and future challenges, respectively. It is obvious that several deep learning models and their variants have been widely applied in different subfields of economics, e.g., financial economics, macroeconomics and monetary economics, agricultural and natural resource economics, industrial organization, urban, rural, regional, real estate and transportation economics, health, education and welfare, business administration and microeconomics, etc. We are very confident that decision-making in economics will be more intelligent with the development of deep learning, because the research of deep learning in economics has become a hot and important topic recently.