Photonic nanocrystals are periodic dielectric or metallic structures having photonic bands in analogy to electronic bands of semiconductors. The presence of photonic band-gaps, where the propagation of photons of certain frequencies is prohibited, and the variety of photon dispersions give rise to novel and unusual optical phenomena. Consequently, photonic crystals are now envisaged as an essential building block of future photonic devices. This paper aims to provide a review of contemporary developments on the physics and applications of photonic crystals with an emphasis on optical properties of coupled microcavity waveguides and on the negative refraction phenomenon. The enhancement of spontaneous emission in a silicon nitride photonic nanocrystal is investigated in detail. Both the negative refraction of a Gaussian beam and the focusing of a microwave point source through a photonic crystal slab with subwavelength resolution are studied experimentally.