This dissertation presents material design strategies to investigate cell-biomaterial interactions on specific biocompatible polymers and polymer blends by using mouse pre-osteoblastic MC3T3 cells aiming for potential applications in bone tissue engineering. Chapter 1 reviews some related background knowledge including polymeric biomaterials for tissue engineering, cell-biomaterial interaction, synthetic photo-crosslinkable and degradable polymers, and the effect of surface features on osteoblast cell responses. Chapter 2 presents photo-crosslinkable composites of poly(propylene fumarate) (PPF), an injectable and biodegradable polyester, and methacryl-polyhedral oligomeric silsesquioxane (mPOSS), which has eight methacryl groups tethered with a cage-like hybrid inorganic-organic nanostructure, for bone tissue engineering applications. Blending mPOSS with PPF was found to decrease the viscosity of PPF, expedite photo-crosslinking process, increase tensile modulus and accelerate hydrolytic degradation of crosslinked PPF/mPOSS while it did not significantly alter surface wettability, protein adsorption, and cell response. Chapter 3 demonstrates a polymer blend composed of amorphous PPF and semicrystalline poly(ε-caprolactone) (PCL), a widely used biocompatible and biodegradable polymer, in both uncrosslinked and photo-crosslinked forms. Thermal, rheological, mechanical properties as well as surface hydrophilicity and morphology can be well controlled by crosslinking density and crystallinity. Distinct cell attachment, spreading, and proliferation have been found to PPF/PCL blends in the presence or absence of cross-links. Chapter 4 and 5 describe the crystallization induced banded spherulitic morphologies in PPF/PCL blends and PCL homo-blends and their preliminary biological evaluation. Thermal properties, crystallization kinetics, and surface morphology of these blends can be regulated by isothermal crystallization temperature and composition. Surface roughness has been found to play an important role in influencing protein adsorption and cell response. Chapter 6 introduces a newly synthesized biodegradable elastomer, poly(ε-caprolactone) triacrylate (PCLTA), with two different molecular weights resulting in distinct mechanical properties at physiological temperature. Using replica molding from silicon wafers, photo-crosslinked PCLTA substrates with concentric micro-grooves have been successfully fabricated. MC3T3 cell attachment, proliferation, and differentiation could be better supported by stiffer substrates while not significantly influenced by micro-groove dimensions. Cell orientation, nuclei shape and localization, mineralization, and gene expression level of osteocalcin have been found to be more significant on narrower micro-grooves when groove depth was 10 μm.