Guided mode resonant (GMR) structures are optical devices that consist of a planar waveguide with a periodic structure either imbedded in or on the surface of the structure. The resonance anomaly in GMR structures has many applications as dielectric mirrors, tunable devices, sensors,and narrow spectral band reflection filters. A desirable response from a resonant grating filter normally includes a nearly 100% narrowband resonant spectral reflection (transmission), and a broad angular acceptance at either normal incidence or an oblique angle of incidence. This dissertation is a detailed study of the unique nature of the resonance anomaly in GMR structures with two-dimensional (2-D) periodic perturbation. Clear understanding of the resonance phenomenon is developed and novel 2-D GMR structures are proposed to significantly improve the performance of narrow spectral filters. In 2-D grating diffraction, each diffracted order inherently propagates in its distinct diffraction plane. This allows for coupled polarization dependent resonant leaky modes with one in each diffraction plane. The nature of the interaction between these non-collinear guides and its impact on spectral and angular response of GMR devices is investigated and quantified for 2-D structures with rectangular and hexagonal grids. Based on the developed understanding of the underlying phenomenon, novel GMR devices are proposed and analyzed. A novel controllable multi-line guided mode resonant (GMR) filter is proposed. The separation of spectral wavelength resonances supported by a two-dimensional GMR structure can be coarse or fine depending on the physical dimensions of the structure and not the material properties. Multiple resonances are produced by weakly guided modes individually propagating along multiple planes of diffraction. Controllable two-line and three-line narrow-band reflection filter designs with spectral separation from a few up to hundreds of nanometers are exhibited using rectangular-lattice and hexagonal-lattice grating GMR structures, respectively. Broadening of the angular response of narrow band two-dimension guided mode resonant spectral filters, while maintaining a narrow spectral response, is investigated. The angular response is broadened by coupling the diffracted orders into multiple fundamental guided resonant modes. These guided modes have the same propagation constant but propagating in different planes inherent in multiple planes of diffraction of the 2-D gratings. The propagation constants of the guided resonant modes are determined from the physical dimensions of the grating (periodicity and duty cycle) and the incident direction. A five-fold improvement in the angular tolerance is achieved using a grating with strong second Bragg diffraction in order to produce a crossed diffraction. A novel dual grating structure with a second grating located on the substrate side is proposed to further broaden the angular tolerance of the spectral filter without degrading its spectral response. This strong second Bragg backward diffraction from the substrate grating causes two successive resonant bands to merge producing a resonance with symmetric broad angular response.