The complexity and internal organization of mammalian cells as well as the regulation of intracellular transport processes has increasingly moved into the focus of investigation during the past two decades. Advanced staining and microscopy techniques help to shed light onto spatial cellular compartmentation and regulation, increasing the demand for improved modeling techniques. In this chapter, we summarize recent developments in the field of quantitative simulation approaches and frameworks for the description of intracellular transport processes. Special focus is therefore laid on compartmented and spatiotemporally resolved simulation approaches. The processes considered include free and facilitated diffusion of molecules, active transport via the microtubule and actin filament network, vesicle distribution, membrane transport, cell cycle-dependent cell growth and morphology variation, and protein production. Commercially and freely available simulation packages are summarized as well as model data exchange and harmonization issues.