Design-by-Analogy (DbA) is a design methodology that draws inspiration from a source domain to a target domain to generate new solutions to problems or designs, which 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 technologies have presented new opportunities for developing data-driven methods and tools for DbA support. Herein, we survey the prior data-driven DbA studies and categorize and analyze individual study according to the data, methods and applications in four categories including analogy encoding, retrieval, mapping, and evaluation. Based on the structured literature analysis, we elucidate the state of the art of data-driven DbA research to date and benchmark it with the frontier of data science and AI research to identify promising research opportunities and directions for the field.