More than a decade ago, the phenomena of long distance propagation and filamentation were discovered in high-power, ultrashort light pulses propagating in gaseous and condensed bulk media. This instigated keen interest and earnest research, motivated by both the basic physics and many practical applications. A great deal of our knowledge concerning these phenomena originates in modeling and numerical simulations. Realistic numerical modeling continues to provide new insights into the underlying physics that would be extremely difficult to understand from experiments alone. Here, I present an overview of numerical methods capable to study the highly nonlinear processes that accompany optical filamentation, such as explosive broadening of spectrum, plasma generation and harmonic generation. I will also discuss an effective nonlinear weave mixing paradigm that provides us with an intuitive yet quantitative way to understand complex experimental data.