  We study RG flows between superconformal field theories living in different
spacetime dimensions which exhibit universal properties, independent of the
details of the UV and IR theories. In particular, when the UV and IR theories
are both even-dimensional we establish exact universal relations between their
conformal anomaly coefficients. We also provide strong evidence for similar
relations between appropriately defined free energies for RG flows between
odd-dimensional theories in the large $N$ limit. Holographically, these RG
flows across dimensions are described by asymptotically AdS black branes in a
gauged supergravity theory, which we exhibit explicitly. We also discuss the
uplift of these solutions to string and M-theory and comment on how the entropy
of such black branes is captured by the dual field theory.
