A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. A fiber Bragg grating can therefore be used as an inline optical filter to block certain wavelengths, or as a wavelength-specific reflector. Fiber Bragg gratings are created by "inscribing" or "writing" systematic (periodic or aperiodic) variation of refractive index into the core of a special type of optical fiber using an intense ultraviolet (UV) source such as a UV laser. A long-period fiber grating couples light from a guided mode into forward propagating cladding modes where it is lost due to absorption and scattering. It is an optical fiber structure with the properties periodically varying along the fiber, such that the conditions for the interaction of several copropagating modes are satisfied. The period of such a structure is of the order of a fraction of a millimeter. In contrast to the fiber Bragg gratings, LPFGs couple copropagating modes with close propagation constants; therefore, the period of such a grating can considerably exceed the wavelength of radiation propagating in the fiber. Because the period of an LPFG is much larger than the wavelength, LPFGs are relatively simple to manufacture. Since LPFGs couple copropagating modes, their resonances can only be observed in transmission spectra. Long period grating has a wide variety of applications, including band-rejection filters, gain flattening filter and sensors. Various gratings with complex structures have been designed: gratings combining several LPFGs, LPFGs with superstructures, chirped gratings, and gratings with apodization. Various LPFG-based devices have been developed: filters, sensors, fiber dispersion compensators, etc. This book entitled Current Trends in Short- and Long-period Fiber Gratings emphasizes the current trends in both short- and long-period fiber grating technology. This book intends to provide highlights of the current topics in this area, showing the recent advances in the field of fiber gratings.