In this review, various achievements in the field of development of tissue-engineered scaffolds with the electrospinning approach were observed. Through the appropriate selection of electrospinning parameters, such as solution viscosity, the type of solvent, voltage, the distance between a tip and a collector etc., scaffolds with a high degree of porosity and pore size applicable for optimal cell infiltration can be obtained. These tissue-like materials can be produced from both synthetic and natural polymers and their mixtures. Based on the characteristics specific for the desirable tissue - vascular, bone or cardiac - materials providing the required mechanical properties, architecture, degradation kinetics and biocompatibility are selected for scaffold synthesis. In different studies, electrospun fibers were modified by adding biologically active agents or nanoparticles. This article also describes the particularities of the extracellular matrix of different tissues and approaches used for specific tissue imitation. Repopulation of the matrices with autologous cells before transplantation is the most commonly used method to improve the biocompatibility of the scaffold and the recipient.