Three-dimensional food printing (3DFP) presents unparalleled opportunities for personalised nutrition, clinical dysphagia management, decentralised on-demand production, and space-mission food provision. However, industrial translation remains constrained by inconsistent rheological characterisation, limited cross-material generalisation of process-control models, and the absence of integrated quality-control frameworks for post-processed and stimulus-responsive constructs. Although extrusion-based 3DFP offers the broadest substrate compatibility among additive manufacturing routes, prior reviews have treated ink formulation, process control, post-processing, and 4D transformation as separate domains. In this work, extrusion-based 3DFP is reviewed in an integrated manner. Rheological foundations and substrate-specific ink design are examined across hydrocolloid, protein, starch, fruit/vegetable, dairy, meat, and bioactive-loaded systems. Intelligent process control is then discussed through three integrated axes: computational fluid dynamics modelling, data-driven low-field NMR with machine-learning prediction, and real-time computer-vision feedback. Pre- and post-processing engineering is examined alongside an integrated quality-control framework, and recent stimulus-responsive 4D studies are organised by trigger and response. Synergistic integration of these domains demonstrates clinical and personalised-nutrition potential beyond that of any single-domain approach. This article systematically reviews the ink design, intelligent process control, post-processing engineering, and stimulus-responsive 4D transformation of extrusion-based 3DFP, aiming to provide valuable insights for the development of intelligent food-printing systems.