In this thesis, we explore the four aspects of fiber Bragg grating sensors: mathematical modeling of Fiber Bragg Grating response/spectral characteristics, fabrication using phase mask, application and interrogation. Applications of fiber Bragg gratings, also known as in-fiber gratings, with emphasis on their sensing capabilities, interrogation of an array of sensors and their performance in structural health monitoring scenario are documented. First, we study the process of photosensitivity phenomenon in glasses, in particular GeO2:SiO2 glasses. For mathematical modeling we consider the 1-D refractive index profile along the propagation axis of an optical fiber drawn from the preform of such glasses. These 1-D index structures exhibit a bandgap for propagation along the fiber axis. We show how the bandgap is dependent on the two structural parameters: index periodicity and effective refractive index. The mathematical model provides the characteristics of three sensor parameters -resonance wavelength also known as the Bragg wavelength (λB ), filter bandwidth (ΔλB ), and reflectivity (R). We show that the evolution of the index structure in germanosilicate glasses is dependent on the inscription parameters such as exposure time, intensity of the laser used for inscribing, the interference pattern, and coherence of the laser system. In particular, a phase mask is used as the diffffacting element to generate the required interference pattern, that is exposed on the photosensitive fiber. We present a mathematical model of the electromagnetic diffraction pattern behind the phase mask and study the effect of the limited coherence of the writing laser on the interference pattern produced by the diffracting beams from the mask. Next, we demostrate the sensing capabilities of the fiber Bragg gratings for measuring strain, temperature and magnetic fields. We report linearity of 99.7% and sensitivity of 10.35pm/◦C for the grating temperature sensor. An array of gratings assigned with non-overlapping spectral windows is inscribed in a single fiber and applied for distributed sensing of structural health monitoring of an aircraft’s composite air-brake panel. The performance of these sensors is compared with the industry standard resistance foil gauges. We report good agreement between the two gauges (FBG and RSG). In some applications it is more desirable to know the spectral content, rather than the magnitude of perturbation. Fiber Bragg gratings sensors can be used to track events that occur in a very small span of time and contain high frequencies. Such applications demand very high speed wavelength demodulation methods. We present two interrogation techniques: wavelength-shift time-stamping (WSTS) and reflectivity division multiplexing (RDM). WSTS interrogation method employs the multiple threshold-crossing technique to quantize the sensor grating fluctuations and in the process produces the time stamps at every level-cross. The time-stamps are assembled and with the a priori knowledge of the threshold levels, the strain signal is reconstructed. The RDM methodology is an extension of the WSTS model to address multiple sensors. We show that by assigning unique reflectivities to each of the sensors in an array, the time-stamps from each of the sensors can be tagged. The time-stamps are collected by virtue of their corresponding pulse heights, and assembled to reconstruct the strain signal of each of the array sensor. We demonstrate that the two interrogation techniques are self-referencing systems, i.e., the speed at which the signals are reconstructed is instantaneous or as fast as the signal itself.