The fabrication of 3D scaffolds is under wide investigation in tissue engineering (TE) because of its incessant development of new advanced technologies and the improvement of traditional processes. Currently, scientific and clinical research focuses on scaffold characterization to restore the function of missing or damaged tissues. A key for suitable scaffold production is the guarantee of an interconnected porous structure that allows the cells to grow as in native tissue. The fabrication techniques should meet the appropriate requirements, including feasible reproducibility and time- and cost-effective assets. This is necessary for easy processability, which is associated with the large range of biomaterials supporting the use of fabrication technologies. This paper presents a review of scaffold fabrication methods starting from polymer solutions that provide highly porous structures under controlled process parameters. In this review, general information of solution-based technologies, including freeze-drying, thermally or diffusion induced phase separation (TIPS or DIPS), and electrospinning, are presented, along with an overview of their technological strategies and applications. Furthermore, the differences in the fabricated constructs in terms of pore size and distribution, porosity, morphology, and mechanical and biological properties, are clarified and critically reviewed. Then, the combination of these techniques for obtaining scaffolds is described, offering the advantages of mimicking the unique architecture of tissues and organs that are intrinsically difficult to design.