The SimpleX radiative transfer method is based on the interpretation of photons as particles interacting on a natural scale: the local mean free path. In our method, light is transported along the... Show moreThe SimpleX radiative transfer method is based on the interpretation of photons as particles interacting on a natural scale: the local mean free path. In our method, light is transported along the lines of an unstructured Delaunay mesh that encodes this natural distance and represents the physical medium. The SimpleX method is fast, highly adaptive and its computational cost does not scale with the number of sources. It is therefore well-suited for cosmological applications where it is essential to cover many orders of magnitude in resolution and where millions of sources can exist within a single simulation. We describe the code, its recent developments and apply it to several relevant astrophysical problems. In particular, we perform radiative transfer calculations of cosmological reionization and of the wind-wind interaction region of the Eta Carinae binary system. Show less