As an important passive optical component, long-period fiber gratings (LPFGs) have all the advantages of optical fiber sensors, such as anti-electromagnetic interference, corrosion resistance, high sensitivity, small volume, and compatible with fiber system, which have wide applications in the field of optical fiber sensors and optical communications. The paper summarizes the principle of mode coupling, the methods of theoretical analysis, fabrication techniques, and applications of the LPFGs in the field of optical fiber sensors and optical communications. The fabrication techniques include the laser inscribing techniques (UV laser, carbon dioxide laser, and femtosecond laser writing techniques) and non-laser techniques (arc discharge, mechanical micro-bending, cladding etching, fusion tapering, ion implantation, and acoustic wave modulation techniques). For the sensing application of the LPFGs, the characteristics of gratings on the temperature, strain, bending, torsion, and surrounding refractive index have been summarized. And their applications as all fiber filter, mode convertor, polarizer, and mode coupler have also been discussed for the applications in optical communication system. The paper is written in a tutorial style. We aim to provide a general reference for students, academics who are going to join in this field.