Stochastic process has a glorious history in physics, chemistry and biology. Due to the advance of single-molecule techniques, stochastic modeling and computation become more and more useful and popular recently. I will talk about several different issues related to stochastic processes at single-molecule and single-cell levels, including stochastic theory of nonequilibrium statistical mechanics, the uncover of the molecular mechanism of transcriptional burst, and the fluctuating-rate model as well as the rate formula for the phenotype transition in an intermediate scenario of a single cell. A series of problems in applied mathematics could also arise from stochastic processes in physics, chemistry and biology.