The regulation of expression states of genes in cells is a stochastic process. The relatively small numbers of protein molecules of a given type present in the cell and the nonlinear nature of chemical reactions result in behaviours, which are hard to predict from first principles. I will discuss simple models and approximations, which allow for, at least some, analytical progress in studying the general principles of how noise on different levels of the regulatory system affects the complex collective characteristics of systems observed experimentally. Specifically, I will consider toy models, which help us understand how the operator state fluctuations influence the steady state properties and lifetimes of attractors of simple gene systems.