Real-world visual search is rarely a single command: users explore, refine, and change their minds. We introduce Contextual Composed Image Retrieval (CoCo-IR), which reformulates instruction-based retrieval as an interactive, multi-turn dialogue. At each turn the model must interpret a new instruction against the entire interaction history (the initial image, every prior instruction, and every intermediate result), so a complex search goal can be decomposed into a sequence of simple, context-aware steps.