To improve fiber optic communication capacity, multicore fiber, a space division multiplexing implementation option, has attracted increasing research interest. At the same time, various new active and passive optical devices based on multicore fibers are emerging. Multicore fiber grating, which can combine the unique advantages of multicore fiber and fiber grating, offers a wide range of possibilities for the design and application of new all-fiber devices in various fields, such as fiber optic communication, fiber optic sensing, and fiber lasers. In this paper, multi-core optical fiber inscription is classified as selective inscription and full-core inscription. Various multi-core fiber grating inscription schemes based on different light sources and different inscription methods are introduced. The technical characteristics of the different schemes are analysed relative to different application scenarios.