Non-equilibrium physics has traditionally dealt mostly with inanimate matter. Yet, in the last decades there has been increasing interest in understanding living systems from this perspective. One example is using the framework and tools of non-equilibrium statistical mechanics and nonlinear physics to study how living organisms composed of many differentiated cells develop from a single initial cell. The dynamic process of multicellular organism development is out of equilibrium, in that it consumes and dissipates energy. It also involves the formation of many precise and complex structures. Herein we review some of the paradigms being used that focus on how these multicellular structures initially emerge at the molecular level.