## 1 Introduction  
The main scope of tissue engineering (TE) is defined as the set of processes to develop biological structures that are able to restore, maintain, or even improve the function of tissues and/or organs [1]. Aiming to meet this challenging goal, multidisciplinary teams are required to work together in the fields of materials engineering and life sciences [2], to successfully employ scaffolds, growth factors, and cells, which represent the widely famous three pillars of TE. Initially, devices were mostly produced from bioinert materials, aiming to achieve adequate mechanical properties, inducing minimal responses from the host tissues. Then, bioengineered constructs were designed to provoke planned reactions at the implant site and follow a certain degradation rate. More recently, there has been emergent research on using smart materials to support and stimulate a better-mimicking tissue with high multicellular functionality [3; 4; 5; 6].  
Three-dimensional (3D) printing has appeared as a useful technique for TE scaffolding to develop constructs with high control over structure geometry and architecture [7; 8]. Its first appearance was reported in 1986 by [PERSON] et al., who used a novel technique called stereolithography [9], able to fabricate 3D structures by curing a resin with a UV source in a layer-by-layer fashion. Throughout the years, several other 3D printing techniques have been developed (Figure 1), e.g., fused deposition modeling [10], selective laser melting [11], and selective laser sintering [12]. All of these share a great advantage over conventional scaffolding techniques, namely, the ability to use computer assisted design--computer assisted manufacturing (CAD-CAM) to customize constructs, and obtain replacements with topologies optimized by using medical imaging approaches [13; 14]. However, conventional 3D matrices have revealed not to be the optimal approach for a number of clinical needs, e.g., tissue defects that change faster than tissue healing, regenerative processes that could be stimulated by electrical or mechanical inputs, body environments in which physicochemical conditions, such pH and temperature, may change over time.  
By including the capability of stimuli responsiveness, four-dimensional (4D) printing has emerged as an intriguing technology able to induce planned changes of the constructs (e.g., shape, stiffness) when triggered by a certain external stimulus [15; 16], thus showing the potential of bridging the gap between the laboratory constructs and native human tissues. Bioprinting is a printing technology that prints cells together with the biomaterial, usually a hydrogel, known as a bioink [17].  
Figure 1: Three main bioprinting technologies: (**a**) laser [18], (**b**) extrusion [19], (**c**) inject printing [20]. Parts of the figure are reprinted from [18; 19; 20]—open access under Creative Commons CC BY 4.0 license.  
Smart biomaterials are at the basis of 4D printing, which, for biomedical applications, may also include printed live cells, thus being defined \"bio\"-printing [21]. Such materials can change shape or properties (e.g., stiffness, color, texture, transparency, energy transfer/conversion, volume) under the influence of external stimuli. Therefore, a clever use of such materials will result in 3D-built scaffolds that can adapt their features to specific applications [22; 23]. As an innovative field, 4D (bio-)printing is suggested to be a promising tool to obtain effective TE therapies in a large number of clinical applications [24]. In the present review, the latest advances in 4D printing of biomaterials are described, by specifically examining the stimuli-responsive mechanisms and their biomedical suitability. 4D (bio-)printing is an emerging topic of investigation and novel points of view are necessary to build up a critical and instructive knowledge in this field [25].