First-stage radiation effects induced in detectors in accelerators, electronic devices and solar arrays in space, shielding materials for spacecraft, materials in nuclear power plants, and in water samples as proxies for biological matter are traditionally studied via Monte Carlo particle transport approaches. In this chapter, we introduce the basic notions of Monte Carlo particle transport and some of the practicalities of the related codes, also mentioning the low energy extension specific to the case of radiation effects in biological matter. Then, we will discuss some applications in the studies of radiation effects in space and planetary missions and in radiobiology, where synergistic studies between the Monte Carlo community and the condensed matter/chemical-physics community are possible.