I will describe some properties of non-Hermitian random matrices and show their deep connections to non-Hermian Hamiltonians and open quantum systems in a large window of their parameter space. I will also discuss another regime of such systems which show properties similar to those of two-dimensional Poisson distributions. Such analysis of complex eigenvalues is expected to play an important role in understanding open systems in general. I will also discuss an isolated dimer model which displays interesting localization-delocalization physics, has connections with random matrices, and possesses a well-defined classical limit.
