The analysis of particle transport problems motivated the development of the Monte Carlo method, as we noted in our earlier chapter on the history of the Monte Carlo method. While Monte Carlo methods are used in virtually all branches of science and engineering, it is still the case that the most prevalent application of Monte Carlo is for the solution of complex problems that are encountered in particle transport applications. For example, the analysis of electron transport for electron beam cancer therapy, or the analysis of photon transport in a cloudy atmosphere, or the attenuation of neutrons in a biological shield. These problems are typically characterized by the following features:

- Complex 3-D and non-Cartesian geometry (e.g., nuclear reactor plant; human body)
- Complex material configurations (e.g., semiconductor chips)
- Complicated physical phenomena due to interaction of radiation (neutrons, photons,...) with medium
- Some known source of radiation incident on (or emitted within) the geometry
- Required output is the amount of radiation, its deposition, or its effect in arbitrary regions
- It is desirable to estimate the uncertainties in the simulation
- The computational effort to carry out the simulation should be reasonable