  We review issues related to conservation laws for gravity with a negative
cosmological constant subject to asymptotically (locally) anti-de Sitter
boundary conditions. Beginning with the empty AdS spacetime, we introduce
asymptotically (locally) AdS (AlAdS) boundary conditions, important properties
of the boundary metric, the notion of conformal frames, and the
Fefferman-Graham expansion. These tools are used to construct variational
principles for AlAdS gravity, to more properly define the notion of asymptotic
symmetry, and to construct the associated boundary stress tensor. The resulting
conserved charges are shown to agree (up to possible choices of zero-point)
with those built using Hamiltonian methods. Brief comments are included on AdS
positive energy theorems and the appearance of a central extension of the
AdS$_3$ asymptotic symmetry algebra. We also describe the algebra of boundary
observables and introduce the anti-de Sitter/Conformal Field Theory (AdS/CFT)
correspondence using only tools from gravitational physics (and without other
input from string theory). Our review focuses on motivations, current status,
and open issues as opposed to calculational details. We emphasize the
relativist (as opposed to particle physics) perspective and assume as
background a standard graduate course in general relativity.
