Tissue engineering is one of the most rapidly developing areas in healthcare. A variety of different fabrication techniques, types of biomaterials, and their modification approaches have been studied lately. Significant progress in the design of artificial matrices has led to an evolution from a simple supporting scaffold to a more sophisticated biomaterial environment. Bioabsorbable materials can be employed to fabricate such complex systems. Ideally, these materials should allow for the prevention of further surgeries in order to avoid the removal of scaffolds, as well as allow for the delivery of desired drugs or growth factors to accelerate body tissue recovery. Polymeric scaffolds as drug delivery carriers play a crucial role in the development of tissue engineering. Targeted drug delivery at a specific site with controlled release rates can lead to the reduction of the required dosage and thus fewer side effects. Bioabsorbable polymers should degrade with the desired rate, eluting the drug at predetermined times, and keeping the drug concentration within the therapeutic window in the release medium. The design of the controlled release device may vary significantly due to the local anatomy and microenvironment. Nevertheless, the microstructure of the scaffolds is preferred to be fibrous for better integration in the body. Moreover, the high surface area to volume ratio of the fibrous scaffolds allows high drug loading amount per unit mass. To gain new knowledge in the field of polymeric drug delivery carriers, this study has been divided into two sections. The first direction of the study is the employment of mathematical modeling for the purpose of studying drug release kinetics from various materials which can be potentially used as drug delivery carriers in tissue engineering. The second direction is the investigation of surface modification approaches for controlling drug release from polymeric materials. The notion of combining theoretical and experimental approaches aimed at the improvement of biomaterial properties is believed to be beneficial, since it creates a multi-angle view on such a complex task. In other words, this combination enables us to look at the current development level of drug delivery systems from different perspectives. In this thesis, the fabrication of bioabsorbable polymeric scaffolds by means of electrospinning was investigated. Plasma treatment technique was studied from a relatively new perspective as a tool for controlled drug release from polymeric biomaterials, and then applied during the fabrication of a model drug delivery system. Two novel mathematical models were proposed to analyse the diffusion of drugs from variously shaped biomaterials. The evidence from this research suggests that the new models can be more accurate in terms of drug diffusion coefficient determination. The work obtained within this thesis has significantly contributed to the improved understanding of the ability to control drug release from diverse biomaterials by means of plasma treatment, and to the refinement of the mathematical modeling tools employed to describe the diffusion processes in these systems for further enhancement of the biomaterials. Novel biomaterials with controlled drug release can become crucial components of the scaffolds for skin, ligament and muscle, liver and kidney, vascular and heart, bone and cartilage tissue engineering.