  The spectral, dynamical and topological properties of physical systems
described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians
are deeply modified by the appearance of exceptional points and spectral
singularities. Here we show that exceptional points in the continuum can arise
in non-Hermitian (yet admitting and entirely real-valued energy spectrum)
optical lattices with engineered defects. At an exceptional point, the lattice
sustains a bound state with an energy embedded in the spectrum of scattered
states, similar to the von-Neumann Wigner bound states in the continuum of
Hermitian lattices. However, the dynamical and scattering properties of the
bound state at an exceptional point are deeply different from those of ordinary
von-Neumann Wigner bound states in an Hermitian system. In particular, the
bound state in the continuum at an exceptional point is an unstable state that
can secularly grow by an infinitesimal perturbation. Such properties are
discussed in details for transport of discretized light in a
$\mathcal{PT}$-symmetric array of coupled optical waveguides, which could
provide an experimentally accessible system to observe exceptional points in
the continuum.
