Actin polymerization and network formation are key processes in cell motility. Numerous actin binding proteins that control the dynamic properties of actin networks have been studied and models such as the dendritic nucleation scheme have been proposed for the functional integration of at least a minimal set of such regulatory proteins. In this talk we will describe recent work on the evolution of the distribution of filament lengths and nucleotide profiles of actin filaments from both the deterministic and stochastic viewpoints. For the latter we develop a master equation for the biochemical processes involved at the individual filament level and simulate the dynamics by generating numerical realizations using a Monte Carlo scheme. A new computational algorithm that is far more efficient than standard methods will also be described.