This paper provides a comprehensive state-of-the-art investigation of the recent advances in data science in emerging economic applications. The analysis is performed on the novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a broad and diverse range of economics research from the stock market, marketing, and e-commerce to corporate banking and cryptocurrency. Prisma method, a systematic literature review methodology, is used to ensure the quality of the survey. The findings reveal that the trends follow the advancement of hybrid models, which outperform other learning algorithms. It is further expected that the trends will converge toward the evolution of sophisticated hybrid deep learning models.