We considered three types of stochastic models of a single population growth: with diffusion-type noise
with parameters replaced by stochastic processes
and with random jumps describing a sudden decrease in population size. We presented methods for studying stochastic processes modeling population growth, in particular, the long-time behavior of sample paths and their distributions. We were especially interested in the asymptotic stability of the density of the distributions of these processes. We gave biological interpretations, examples, and numerical simulations of theoretical methods and results.