  The various roles of boundary terms in the gravitational Lagrangian and
Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is
ideally suited for a large class of quasilocal energy-momentum expressions for
general relativity. This approach provides a physical interpretation for many
of the well-known gravitational energy-momentum expressions including all of
the pseudotensors, associating each with unique boundary conditions. From this
perspective we find that the pseudotensors of Einstein and M{\o}ller (which is
closely related to Komar's superpotential) are especially natural, but the
latter has certain shortcomings. Among the infinite possibilities, we found
that there are really only two Hamiltonian-boundary-term quasilocal expressions
which correspond to {\em covariant} boundary conditions; they are respectively
of the Dirichlet or Neumann type. Our Dirichlet expression coincides with the
expression recently obtained by Katz and coworkers using Noether arguments and
a fixed background. A modification of their argument yields our Neumann
expression.
