Holography relates gravity in asymptotically locally hyperbolic manifolds to conformal field theories in one less dimension. This talk will focus on recent developments in holography that may be of particular interest to mathematicians and relativists. Topics covered will include (i) generalisations of holography to different classes of spacetime asymptotics (ii) minimal surfaces in hyperbolic geometries, their renormalised areas and entanglement and (iii) relation between Bondi-Sachs and Fefferman-Graham analysis of asymptotic structure.