AdS₂ has an SL(2,R) isometry group. It is argued that in the context of quantum gravity on AdS₂ this group is enlarged to the full infinite-dimensional 1+1 conformal group. Massive scalar fields are coupled to AdS₂ gravity and shown to have associated conformal weights h(m) shifted by their mass. For integral values of h primary boundary operators are obtained as h normal derivatives of the scalar field. AdS₂ string theories arise in the `very-near-horizon' limit of S¹-compactified AdS₂ string theories. This limit corresponds to energies far below the compactification scale. The dual conformal field theory has one null dimension and can in certain cases be described as the discrete light cone quantization of a two-dimensional deformed symmetric-product conformal field theory. Evidence is given that the AdS₂ Virasoro algebra is related to the right-moving AdS₂ Virasoro algebra by a topological twist which shifts the central charge to zero.