Fibrous scaffolds based on (bio)polymers are observed as mimicking the microstructure of the extracellular matrix. Thus, they are considered as an example of a utilitarian scaffold, useful for the regeneration of various types of tissues. The techniques described in the literature are well known to obtain submicrometric and nanometric fibers that, when randomly arranged, mimic the ECM. The biomimetic scaffold criterion might be even better reflected if the cell adhesion sites are present on the surface of such fibers. They promote the formation of the focal adhesion contact or facilitate the formation of a protein film on the fiber surface. Such a process is enhanced by an appropriate physical or chemical modification that activates the protein adsorption and the subsequent cell adhesion. The aim of this paper is to present different methods of physical and/or chemical modifications of fibrous materials: which can serve as scaffolds to support the regeneration processes of various tissues. In terms of physical methods, only weak interactions between the surface and the modifier were observed. This technique is simple but not durable. Chemisorption used as a second method of fiber modification is possible if a covalent or ionic bond is formed between the fiber and the modifier. Therefore, the chemical adsorption may not be fully reversible and requires a sequence of chemical actions to form a chemical bond. The most commonly used methods are the combined methods where the first step is the physical activation of the fiber surface, which facilitates the chemical modification step.