The manufacturing and spectral features of different types of long period fiber gratings (LPFGs), ranging from phase-shifted, turn-around point, and internally tilted gratings, to pseudo-random gratings, are described and discussed in detail. In this paper, we rigorously deduce the coupled-mode equations of a long-period fiber grating and fiber Bragg grating in their cascaded structure (CLBG), based on coupled-mode theory. Mistakes in previous. Institute of Applied Physics “Nello Carrara”, National Research Council of Italy (IFAC-CNR), Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy Author to whom correspondence should be addressed.