1089032processes such as direct ink writing (DIW) and droplet printing, which enables to create voxelated matters or devices in 3D with tunable functionalities . To date, intensive efforts are devoted to the functional design of additively manufactured composites, including mechanical [10,11], acoustic , electromagnetic metamaterials [13,14], thermally and electrically conductive structures , water treatment , etc. AM techniques offer the opportunity to create artificial and structural ma-terials with unusual properties in nature such as negative Poisson ratio, negative thermal expansion, negative reflection index . Therefore, different types of metamaterials and digital composites with extraordi-nary mechanical, electromagnetic, and acoustic performances are developed using AM techniques in recent years. However, the reliability and feasibility of multi-material or multi-process AM still remain chal-lenges toward function-driven fabrication. The key route to solve this issue is unifying numerical-driven, and data-driven design strategies, such as topology optimization (TO) and machine learning algorithms with the Process-Structure-Properties-Performance (PSPP) relationship of a multi-material or composite AM process [18–20]. Specifically, a numerical optimization method can be applied on multiple design scales to update the parameters on micro, meso, and macroscale of AM fabri-cated polymetric composites. To summarize those recent research efforts, this work aims to pro-vide a comprehensive review on AM-fabricated polymeric composites, ranging from material processing to their structural design. Comparing to those existing reviews [1,7] on AM fabricated polymeric composites, this paper has three unique aspects: 1) AM techniques available to polymeric composites are briefly discussed in the aspects of their forming mechanisms, feedstock materials, potentials, and constraints of processes; 2) AM-driven material and structural designs of polymeric composites in multiscale are emphasized to establish the comprehensive understanding of PSPP relationship; 3) advances in digital composites, data-driven design/process planning/monitoring of composite, and composite 4D printing are addressed to reveal the opportunities and perspectives. Ultimately, this work provides insights for future research to bridge the gaps between advanced process and digital design, and fully explore the potentials of AM-fabricated composites in a wide range of applications. 2. AM of polymeric composites The conventional classification of AM processes follows ISO/ ASTM52900 standard . Herein, additively manufactured polymeric composites can be broadly classified into continuous fiber and discon-tinuous (short) composites and voxelated polymeric composites [22–24]. The continuous-fiber reinforced composites via conventional pultrusion and continuous compression molding are well-known light-weight materials as load-bearing structures for the applications of aerospace, automobile, sports, etc [25–28]. However, continuous-fiber reinforced polymeric composites have been rarely manufactured by AM, most notably material extrusion process (e.g. fused filament fabri-cation (FFF)) and sheet lamination process (e.g. laminated objective manufacturing (LOM)) [29–31]. In comparison, short-fiber reinforced composites have been manufactured by most AM technologies, including material extrusion processes, powder bed fusion processes, vat photopolymerization processes, binder jetting, material jetting, and other alternative hybrid layer-by-layer approaches [32,33]. Voxelated polymeric composites are uniquely manufacturable by AM approaches such as PolyJet (material jetting), multiple jet fusion (MJF, powder bed fusion), and DIW (material extrusion process) [23,34,35]. In the following content, we are going to use a detailed process name such as FFF, DIW instead of its standard category’s name such as material extrusion since they can more precisely describe unique features of these processes. Thermoplastics and thermosets are two categories of polymer matrices, which are mainly incorporating with reinforcements to form multiphase composites or digital arrangement in space to generate multimaterial voxelated matter [23,36–38]. The thermoplastics are pre-processed in the form of a filament or powders as feedstock mate-rials and applied in FFF and powder-based processes such as selective laser sintering (SLS) and MJF [39,40]. On the other hand, the UV-curable and thermal-curable thermoset resins are employed as raw materials for the AM processes, including DIW, reactive extrusion, stereolithography (SLA), inkjet, and PolyJet [9,41–43]. Both thermo-plastic and thermoset can be used to incorporate with continuous-fibers to form prepreg tape and then applied in the automated fiber placement (AFP) or LOM process [30,44–46]. 2.1. Extrusion-based process Extrusion-based AM is a versatile approach to construct 3D objects layer-by-layer using various types of feedstock materials, including thermoplastic filaments and pellets, highly viscous hydrogel, and viscoelastic inks of thermosets, etc . This is because the different designs of printing nozzles are adopted into the extrusion system. In principle, extruders, syringes, and other printheads are used to deliver materials with external pressures which can be generated by mechanical force, piezoelectrical stimulation, or pneumatic pressure [48,49]. Due to the unique design for particular printing nozzles, the specific form of feedstocks is selected to adapt to the corresponding extrusion system. Most of the extrusion-based processes can be applied to manufacture short-fiber reinforced polymeric composite. Whereas continuous fibers can be only blended with thermoplastics or thermoset precursors before mechanical extrusion in FFF and DIW. Apart from the feedstock materials, the success of the extrusion- based process of polymeric composites depends on multiple process parameters, including feeding speed, melting temperature, chemical composition, fiber loading, the aspect ratio of fiber, depositing speed, and temperature gradients. The distribution of short fibers and the arrangement of long fibers are engineered by the formulated materials and process patterning, which significantly influence the design strate-gies to optimize the structural performances of printed parts . The relationships of PSPP of different composites via extrusion-based pro-cesses are addressed here. 2.1.1.Fused filament fabrication FFF is a type of material extrusion AM process [43,51]. It employs a thermoplastic filament to feed into the heated printing nozzle and extrude the molten material onto a deposition bed with a computer pre-programmed printing path in a layer-by-layer manner as shown in Fig. 1a . Support structures, using soluble polymers in water or acid, are introduced to improve the surface finish of products and increase the complexity of geometry. The common thermoplastics available to FFF candidate materials mainly include amorphous polymers e.g., polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), acrylonitrile styrene acrylate, polycarbonate (PC), polystyrene (PS), and a few semi-crystalline polymers e.g., nylon and polyaryletherketone (PAEK) family, polyphenylene (PPS) and polyphenylsulfone (PPSU) [52,53]. These high-performance thermoplastics usually require a high-pressure extruder and heated process chamber to ensure the fluent flow of viscous materials and avoid part warping upon the chamber cooling. The key factors are addressed in a viscoelastic model of FFF to ensure the quality of printed products, including (1) pressure-driven extrusion flow, (2) bead formation, (3) bead functionality, and (4) component functionality . This model can effectively evaluate the influence of compositional variations and identify appropriate processing parameters, which have been demonstrated for specific materials on FFF and large-scale extrusion platforms . Short fibers and continuous fibers can be adopted by the FFF system to build anisotropic composites as illustrated in Fig. 1d–f [58,59]. Large-scale extrusion AM (industrial-scale platform in several meters in three dimensions) is developed for thermoplastics and other composites at high production rates as shown in Fig. 1b [22,56]. A S. Yuan et al.