© 2014, European Optical Society (EOS). All rights reserved.Much attention has been paid to photonic applications based on periodic media. Meanwhile, quasi-periodic and disordered media have extended the research domain and provided additional novelties for manipulating and controlling light propagation. This review article attempts to highlight the benefits of symmetry reduction in highly symmetric periodic photonic media, and applies the concept of chirality to all-dielectric materials arranged in special orders. Two-dimensional periodic structures known as photonic crystals (PCs) are highly symmetric in terms of structural patterns, due to the lattice types and shape of the elements occupying the PC unit-cell. We propose the idea of intentionally introducing reduced-symmetry, to search for anomalous optical characteristics so that these types of PCs can be used in the design of novel optical devices. Breaking either translational or rotational symmetries of PCs provides enhanced and additional optical characteristics such as creation of a complete photonic bandgap, wavelength demultiplexing, super-collimation, tilted self-collimation, and beam deflecting/routing properties. Utilizing these characteristics allows the design of several types of photonic devices such as polarization-independent waveguides, wavelength demultiplexers, beam deflectors, and routers. Moreover, reducing the symmetry in the PC unit-cell scale produces a novel feature in all-dielectric PCs that is known as chirality. On the basis of above considerations, it is expected that low-symmetric PCs can be considered as a potential structure in photonic device applications, due to the rich inherent optical properties, providing broadband operation, and being free of absorption losses.