Branching processes constitute a special type of stochastic model that are emerging as powerful tool for studying and understanding biological systems. This chapter explores the basis of the branching processes formalism, introducing the fundamental concepts of the Galton-Watson framework and its more biologically relevant extensions. We then present specific biological scenarios and examples, ranging from population growth to disease spreading and evolutionary dynamics. Finally, we provide a detailed description of our own extension of the framework to study the dynamics of organogenesis in the context of stem cell decisions. By simplifying the complexity of stem cell differentiation as a simple branching process in which cells divide via either symmetric or asymmetric types of divisions, we derive analytical solutions that enable us to quantify changes in the balance between self-renewal and terminal specification that occur during development. This chapter aims to inspire researchers to leverage the power and simplicity of branching processes as an alternative or complementary approach to studying complex biological systems.