Long-period fiber gratings (LPFGs) are efficient ways to achieve high-order core mode conversion and vortex mode conversion in few-mode fibers (FMFs), which have the benefits of flexible structure, high integration, low insertion loss, and strong wavelength selectivity. With the rapid development of mode division multiplexing (MDM) optical communications, the FMF-LPFGs could have promising applications in the field of MDM optical communications and optical sensors. In this paper, we briefly introduce the principle of optical coupling, theoretical analysis, fabrication techniques, and applications of the FMF-LPFGs in optical communications and optical sensors. The CO2-laser writing technique and arc discharge technique are widely used for the fabrication of FMF-LPFGs and FMF helical long-period gratings (HLPGs). The hydrogen-oxygen flame technique has the advantage on the fabrication of FMF-HLPGs. The mechanical micro-bending and acoustic induction techniques are flexible and effective methods in fundamental researches. The femtosecond laser technique has the advantages for the fabrication of parallel FMF-LPFGs and micro-structure FMF-LPFGs. The mode converters based on the FMF-LPFGs have been demonstrated using different inscription techniques. The FMF-LPFG converters have the advantages such as temperature insensitivity and wavelength tunability. The broadband converters have been demonstrated based on the phase-shift FMF-LPFG, cascaded FMF-LPFGs, and FMF-LPFG operating at dispersion turning point. The FMF-LPFGs and FMF-HLPGs are an excellent option to generate all-fiber orbital angular momentum (OAM) modes in different specialty FMFs, especially the FMF-HLPGs can excite different-order OAM modes directly. As the novel fiber component, the sensing application of FMF-LPFGs and FMF-HLPGs is also briefly introduced.