  We study aspects of anti-de Sitter space in the context of the Swampland. In
particular, we conjecture that the near-flat limit of pure AdS belongs to the
Swampland, as it is necessarily accompanied by an infinite tower of light
states. The mass of the tower is power-law in the cosmological constant, with a
power of $\frac{1}{2}$ for the supersymmetric case. We discuss relations
between this behaviour and other Swampland conjectures such as the censorship
of an unbounded number of massless fields, and the refined de Sitter
conjecture. Moreover, we propose that changes to the AdS radius have an
interpretation in terms of a generalised distance conjecture which associates a
distance to variations of all fields. In this framework, we argue that the
distance to the $\Lambda \rightarrow 0$ limit of AdS is infinite, leading to
the light tower of states. We also discuss implications of the conjecture for
de Sitter space.
