Design-by-analogy (DbA) is a design methodology wherein new solutions, opportunities, or designs are generated in a target domain based on inspiration drawn from a source domain; it can benefit designers in mitigating design fixation and improving design ideation outcomes. Recently, the increasingly available design databases and rapidly advancing data science and artificial intelligence (AI) technologies have presented new opportunities for developing data-driven methods and tools for DbA support. In this study, we survey existing data-driven DbA studies and categorize individual studies according to the data, methods, and applications into four categories, namely, analogy encoding, retrieval, mapping, and evaluation. Based on both nuanced organic review and structured analysis, this paper elucidates the state-of-the-art of data-driven DbA research to date and benchmarks it with the frontier of data science and AI research to identify promising research opportunities and directions for the field. Finally, we propose a future conceptual data-driven DbA system that integrates all propositions.