  The search for new computational machines beyond the traditional von Neumann
architecture has given rise to a modern area of nonlinear science --
development of unconventional computing -- requiring the efforts of
mathematicians, physicists and engineers. Many analogue physical systems
including nonlinear oscillator networks, lasers, and condensates were proposed
and realised to address hard computational problems from various areas of
social and physical sciences and technology. The analogue systems emulate spin
Hamiltonians with continuous or discrete degrees of freedom to which actual
optimisation problems can be mapped. Understanding the underlying physical
process by which the system finds the ground state often leads to new classes
of system-inspired or quantum-inspired algorithms for hard optimisation.
Together physical platforms and related algorithms can be combined to form a
hybrid architecture that may one day compete with conventional computing. In
this Chapter, we review some of the systems and physically-inspired algorithms
that show such promise.
