The creation of periodic structures in nano- or micro-scale is an exciting challenge of materials science. Meanwhile, the structures with alternating periodic dielectric constants, known as photonic crystals, are great potentials for many applications in optical integrated circuits. In this dissertation, we design and fabricate periodic two- (2D) and three-dimensional (3D) photonic microstructures with desired symmetry, scalable size or novel functionality (e.g. anisotropic feature) using holographic lithography (HL) technique and via harnessing mechanical instability in different polymer systems. In fabrication of 3D diamond-like photonic structure via four-beam single-exposure HL, we quantitatively analyze the lattice distortion due to refraction effect and photoresist shrinkage, which decreases the symmetry of the resulting structure, thus degrading the quality of photonic bandgap (PBG) properties. To address the optical challenge in fabrication of a perfect 3D photonic crystal using four-beam single-exposure HL approach, we design dual-beam triple-exposure HL and fabricate size-scalable diamond-like structure with minimal distortion. We also investigate the robustness of the optical setup, and find that for a large size structure, a small deviation of beam angles may lead to a significant change of lattice size whereas the translational symmetry of SU-8 structure remains reasonably close to face-center-cubic. Besides the 3D holographic fabrication, we develop an efficient method to create a rich library of 2D photonic structures with anisotropic unit cells via harnessing of pattern transformation of an elastomeric poly(dimethylsiloxane) (PDMS) membrane. We then study the PBG properties of 2D Si post arrays with structural symmetries same as those deformed 2D photonic structures, and their tolerance to the structural deviation. To reveal the underlying mechanisms of pattern transformation and the potential for highly ordered complex structures, we systematically study the kinetic process of capillary induced pattern transformation and recovery when swelling and drying 2D poly(2-hydroxyethyl methacrylate) (PHEMA) membranes with a square lattice of micron-sized cylindrical holes from water repeatedly. We find that the PHEMA membrane undergo different modes of instability during drying: when the internal tension is low, the hole reduces size but retains the shape, in a mode of breathing; when the tension is high, the square lattice bifurcated into a diamond plate pattern with neighboring slits perpendicular to each other, in a mode of buckling. Meanwhile, there are many antiphase boundaries (APBs) formed in the diamond plate pattern, where the morphology (either random or aligned) is dependent on the moving speed of the water front. Using dynamic Monte Carlo method we simulate the nucleation, growth and APB formation in pattern transformation and recovery processes, which matches qualitatively with the experimental results. Finally, we suggest a new strategy of shaping the APBs toward the creation of a single crystal transformed pattern.