The first few days of embryonic development in eutherian mammals are dedicated to the specification and elaboration of the extraembryonic tissues. However, where the fetus ends and its adnexa begins is not always as self-evident during the early stages of development, when the definitive body axes are still being laid down, the germ layers being specified and a discrete form or bodyplan is yet to emerge. Function, anatomy, histomorphology and molecular identities have been used through the history of embryology, to make this distinction. In this review, we explore them individually by using specific examples from the early embryo. While highlighting the challenges of drawing discrete boundaries between embryonic and extraembryonic tissues and the limitations of a binary categorization, we discuss how basing such identity on fate is the most universal and conceptually consistent. This article is part of the theme issue 'Extraembryonic tissues: exploring concepts, definitions and functions across the animal kingdom'.