Unlike the conventional techniques used to construct a tissue scaffolding, three-dimensional (3D) bioprinting technology enables fabrication of a porous structure with complex and diverse geometries, which facilitate evenly distributed cells and orderly release of signal factors. To date, a range of cell-laden materials, such as natural or synthetic polymers, have been deployed by the 3D bioprinting technique to construct the scaffolding systems and regenerate substitutes for the natural extracellular matrix (ECM). Four-dimensional (4D) bioprinting technology has attracted much attention lately because it aims to accommodate the dynamic structural and functional transformations of scaffolds. However, there remain challenges to meet the technical requirements in terms of suitable processability of the bioink formulations, desired mechanical properties of the hydrogel implants, and cell-guided functionality of the biomaterials. Recent bioprinting techniques are reviewed in this article, discussing strategies for hydrogel-based bioinks to mimic native bone tissue-like extracellular matrix environment, including properties of bioink formulations required for bioprinting, structure requirements, and preparation of tough hydrogel scaffolds. Stimulus mechanisms that are commonly used to trigger the dynamic structural and functional transformations of the scaffold are analyzed. At the end, we highlighted the current challenges and possible future avenues of smart hydrogel-based bioink/scaffolds for bone tissue regeneration.