Bilayer graphene (BLG) has recently been used as a tool to stabilize encapsulated single sheets of various layered materials and tune their properties. It was also discovered that the protecting action of graphene sheets makes it possible to synthesize completely new two-dimensional materials (2DMs) inside the BLG by intercalating various atoms and molecules. In comparison to the bulk graphite, BLG allows for easier intercalation and a much larger increase in the interlayer separation of the sheets. Moreover, it enables studying the atomic structure of the intercalated 2DM by using high-resolution transmission electron microscopy. In this review, we summarize the recent progress in this area, with a special focus on new materials created inside BLG. We compare the experimental findings with the theoretical predictions, pay special attention to the discrepancies, and outline the challenges in the field. Finally, we discuss unique opportunities offered by intercalation into 2DMs beyond graphene and their heterostructures.