Mechanosensing and mechanotransduction pathways between the Extracellular Matrix (ECM) and cells form the essential crosstalk that regulates cell homeostasis, tissue development, morphology, maintenance, and function. Understanding these mechanisms involves creating an appropriate cell support that elicits signals to guide cellular functions. In this context, polymers can serve as ideal molecules for producing biomaterials designed to mimic the characteristics of the ECM, thereby triggering responsive mechanisms that closely resemble those induced by a natural physiological system. The generated specific stimuli depend on the different natural or synthetic origins of the polymers, the chemical composition, the assembly structure, and the physical and surface properties of biomaterials. This review discusses the most widely used polymers and their customization to develop biomaterials with tailored properties. It examines how the characteristics of biomaterials-based polymers can be harnessed to replicate the functions of biological cells, making them suitable for biomedical and biotechnological applications.