Labor shortages and the push for higher greenhouse efficiency have accelerated interest in automated harvesting. However, the development of a universal harvesting robot has been constrained by large variations in crop architecture, especially plant height. In this review, a height-based stratification of greenhouse harvesting robots and transferable high-wire crop harvesters is presented, covering ground-level crops (1.5 m, e.g., trellised cucumber). For each height layer, key design features, technical progress, prototype performance, and common obstacles—including fruit occlusion, mechanical crop damage, unreliable operation, and high commercial costs—are analyzed. Future efforts should target intelligent perception, soft end-effectors, and height-specific solutions (swarm robotics for ground crops, modular hybrid designs for medium crops, infrastructure co-design for high-wire crops). By using plant height as the primary stratification criterion, a design-oriented framework is provided, distinct from conventional crop-type or mechanism-based categorizations.