"In order to fully understand and exploit the potential of LPFGs in PCFs, a theoretical and experimental study of LPFGs with a practical modeling of guided modes in PCFs have to be performed. This is the motivation of this work which is based on previous independent extensive studies of LPFGs [7, 8, 9] and PCFs [2, 3]. Specifically, we study the properties of LPFGs induced mechanically in PCFs. In this work, the chapters are organized in such a way that they follow the principal concepts mentioned above. In Chapter 1, the physical theory of long-period fiber gratings and their fabrication’s mechanisms are presented in a detailed way focusing in the mechanical fabrication method. In Chapter 2, a general context about PCFs is presented including a review of the development of PCFs and the description of their principal properties. Furthermore, a description of the numerical methods used to model these kind of fibers is presented focusing principally on the Fast-Fourier-Transform (FFT) mode solver which is performed in this work. Chapter 3 describes new properties of LPFGs obtained as a result of the characterization of different configurations of LPFGs induced mechanically in PCFs. Chapter 4 shows direct applications of these new spectral properties in order to improve the performance of fiber lasers and sensors, and finally, Chapter 5 summarizes all the results obtained and suggests direction for future work."