  Classical Hamiltonian systems with balanced loss and gain(BLG) are considered
in this review. A generic Hamiltonian formulation for systems with
space-dependent BLG is discussed. It is shown that the loss-gain terms may be
removed completely through appropriate co-ordinate transformations with its
effect manifested in modifying the strength of the velocity-mediated coupling.
The effect of the Lorentz interaction in improving the stability of classical
solutions as well as allowing a possibility of defining the corresponding
quantum problem consistently on the real line, instead of within Stokes wedges,
is also discussed. Several exactly solvable models based on translational and
rotational symmetry are discussed which include, coupled cubic oscillators,
Calogero-type inverse-square interaction, Landau Hamiltonian etc. An example of
Hamiltonian chaos within the framework of a model of coupled Duffing oscillator
with BLG is discussed. The role of ${\cal{PT}}$-symmetry on the existence of
periodic solution in systems with BLG is critically analyzed. It is conjectured
that a non-${\cal{PT}}$-symmetric system with BLG may admit periodic solution
if the linear part of the equations of motion does not contain any velocity
mediated interaction and is necessarily ${\cal{PT}}$ symmetric - the nonlinear
interaction may or may not be ${\cal{PT}}$-symmetric. Results related to dimer
and nonlinear Schr$\ddot{o}$dinger equation with BLG are mentioned briefly.
