This talk will introduce stochastic modeling and simulation of biochemical processes. Stochasticity may play an important role in case the copy number of some component involved in the biochemical processes is small. Stochastic models for biochemical processes using continuous-time Markov jump processes and stochastic differential equations are considered. In this talk, I will show several examples in biology and their stochastic models. The first part of the talk is about stochastic models in the spatially-homogeneous biological systems. Modeling of biochemical oscillators and cancer signaling pathways will be discussed. In this part, multiscale approximations of chemical reaction networks will be introduced which help to reduce the network complexity using various scales in species numbers and reaction rates. The second part of the talk is about stochastic models in the spatially-distributed biological systems. Two examples in biology and the models will be introduced: the glycolytic pathway in the distributed system and pattern formation in developmental biology. These examples will show how stochasticity will change the biological systems in different ways.