Recently synthesized MoSi₂N₄ is the first septuple-layer two-dimensional material, which does not naturally occur as a layered crystal, and has been obtained with chemical vapour deposition growth. It can be considered as MoN₂ crystal (with a crystal structure of MoS₂) intercalating Si₂N₂ two-dimensional layer (with the structure similar to InSe). The discovery of this material has spurred on research into its electronic properties, and also to the prediction and classification of dozens of other members of the family. Whereas the originally synthesized MoSi₂N₄ is a semiconductor, some of the members of the family are also metallic, some are magnetic, some showing remarkable properties, such as very high room-temperature electron mobilities. The major interest towards these materials is coming from the septuple-layer structure, which allows not only multiple crystal phases but also complex compositions, in particular those with broken mirror-reflection symmetry against the layer of metal atoms. In this Review, we provide a profile of this new family of materials and discuss the possibilities they open up towards new physics and applications.