Three-dimensional (3D) printing is a valuable tool in the production of complexes structures with specific shapes for tissue engineering. Differently from native tissues, the printed structures are static and do not transform their shape in response to different environment changes. Stimuli-responsive biocompatible materials have emerged in the biomedical field due to the ability of responding to other stimuli (physical, chemical, and/or biological), resulting in microstructures modifications. Four-dimensional (4D) printing arises as a new technology that implements dynamic improvements in printed structures using smart materials (stimuli-responsive materials) and/or cells. These dynamic scaffolds enable engineered tissues to undergo morphological changes in a pre-planned way. Stimuli-responsive polymeric hydrogels are the most promising material for 4D bio-fabrication because they produce a biocompatible and bioresorbable 3D shape environment similar to the extracellular matrix and allow deposition of cells on the scaffold surface as well as in the inside. Subsequently, this review presents different bioresorbable advanced polymers and discusses its use in 4D printing for tissue engineering applications.