The generation of single photons in the mid-infrared spectral region is attracting the interest of scientific and technological research, motivated by the potential improvements that many important and emerging applications, such as quantum sensing, metrology and communication, could benefit from. This review reports the progress in short and mid-infrared single photon generation, focusing on probabilistic sources based on the two non-linear processes of spontaneous parametric downconversion (SPDC) and four wave mixing (FWM). On one hand, numerical simulations of mid-infrared SPDC are described as a powerful tool to assist and guide the experimental realization, along with the implementation and engineering of novel non-linear materials. On the other hand, the advantages offered by FWM in silicon waveguides in terms of integration, miniaturization and manufacturability are presented, providing an optimal technology for integrated quantum applications.