Surface topography is known to be important in biomedical applications such as scaffolds for tissue regeneration and has been shown to affect wettability and cell behaviour. Traditionally, topographical effects such as surface texturing have been generated using methods such as photolithography, soft lithography, thermal embossing, and laser/electron beam techniques. This thesis introduces a relatively new technique known as photoembossing to create surface texturing for biomedical applications. Photoembossing is used to produce surface texturing on polymer surfaces by patterned ultraviolet (UV) exposure of a photopolymer blend without an etching step or an expensive mould. After a short general introduction and a literature review, the first experimental chapters describe surface patterning of poly(methyl methacrylate) (PMMA) photopolymer substrates by photoembossing. PMMA is blended with an acrylate monomer and photoinitiator by dissolution in a volatile solvent and processed into films by wire bar coating, and fibres are produced by electrospinning. Surface texture is achieved on both films and fibres by photoembossing. Endothelial cell culture shows that the substrates are biocompatible and cells readily adhere to the surface. In tissue regeneration applications, scaffold degradation is often important to allow tissue in-growth. Thus, in subsequent studies polylactide-co-glycolide (PLGA) is used as a polymer binder. PLGA blended with a triacrylate monomer showed partial degradation after 10 weeks, with a cross-linked acrylate network remaining. Endothelial cell adhesion was even better on the PLGA photopolymer substrates compared to PMMA. Furthermore, surface texture improved cell adhesion and proliferation on the PLGA photopolymer. To obtain completely degradable substrates, thiol monomer was used in addition to the acrylate to produce ester bonds after the thiol-ene reaction, which is cleavable by hydrolysis. Accelerated degradation in sodium hydroxide (NaOH) showed complete degradation of this photopolymer system. The degradation rate of the photopolymer could be tuned by the molecular weight of the acrylate monomer, with low molecular weight monomers degrading more slowly than high molecular weight species. Furthermore, the height of the surface relief structures could be enhanced by using low-molecular-weight acrylate monomers. Endothelial cell culture revealed biocompatibility of the blend and cells were able to adhere after 24 hours of seeding. This thesis demonstrates that photoembossing is a viable technique in producing surface texture for tissue engineering applications. This surface texture can be achieved on both biocompatible and biodegradable photopolymer films and fibres.