Two important classes of symmetries are investigated within the framework of optics; parity-time (PT) symmetry and supersymmetry (SUSY). It is shown that PT-symmetric optical structures can exhibit interesting properties which are otherwise unattainable in Hermitean systems. Floquet-Bloch analysis of periodic PT-symmetric potentials is presented and mode selection property of PT-symmetric laser systems is discussed. Additionally, notions from supersymmetry are applied to one- and two-dimensional optical structures in order to explore novel applications based on the design of systems that exhibit similar guided mode and scattering characteristics. Such devices can be exploited for selective mode filtering applications.