Three-dimensional bioprinting is moving beyond anatomical fabrication toward systems that can respond to biological cues, use process data to guide manufacturing, and support patient-specific applications. Rather than treating every responsive material, artificial-intelligence model, or sensor-equipped platform as intelligent, this review uses four descriptive functions—responsiveness, observability, decision capability, and actuation—to compare the field across three operational categories: responsive components, intelligence-assisted systems, and validated closed-loop systems. These functions are not cumulative prerequisites: responsiveness can exist without sensing, and closed-loop control can operate without a responsive bioink. We synthesize smart bioinks and printing quality, intelligent strategy selection, data-driven monitoring and feedback, post-printing maturation, and regenerative or precision-therapeutic applications. Representative evidence indicates that the most credible closed loops currently address fast manufacturing variables such as extrusion and geometry, whereas biological feedback over hours to weeks, continuously updated digital twins, and high-level autonomy remain early. We also distinguish the evidence needs of implantable regenerative constructs from those of patient-derived drug-testing models. The contribution of this review is therefore a cross-domain functional classification and translational evidence hierarchy, rather than a claim that smart materials, AI-assisted design, or closed-loop bioprinting are themselves new.