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While the proliferation of foundation models has significantly boosted individual productivity, it also introduces a potential challenge: the homogenization of creative content. In response, we revisit Design-by-Analogy (DbA), a cognitively grounded approach that fosters novel solutions by mapping inspiration across domains. However, prevailing perspectives often restrict DbA to early ideation or specific data modalities, while reducing AI-driven design to simplified input-output pipelines. Such conceptual limitations inadvertently foster widespread design fixation. To address this, we expand the understanding of DbA by embedding it into the entire creative process, thereby demonstrating its capacity to mitigate such fixation. Through a systematic review of 85 studies, we identify six forms of representation and classify techniques across seven stages of the creative process. We further discuss three major application domains: creative industries, intelligent manufacturing, and education and services, demonstrating DbA's practical relevance. Building on this synthesis, we frame DbA as a mediating technology for human-AI collaboration and outline the potential opportunities and inherent risks for advancing creativity support in HCI and design research.