We reexamine in detail the various processes undergone by positrons in the ISM from their birth to their annihilation using the most recent results of positron interaction cross sections with H, H2 and He. The positrons lives are divided into two phases: the in-flight phase and the thermal phase. The first phase is treated with a Monte Carlo simulation that allows us to determine the fraction of positrons that form positronium and annihilate as well as the characteristics of the annihilation emission as a function of the medium conditions. The second phase is treated with a binary reaction rate approach, with cross sections adopted from experimental measurement or theoretical calculations. An extensive search and update of the knowledge of positron processes was thus undertaken. New reaction rates and line widths have been obtained. We investigate the treatment of the complicated interactions between positrons and interstellar dust grains. New reaction rates and widths of the line resulting from the annihilation inside and outside of the grain have been obtained. The final results of our calculations showed that dust is only important in the hot phase of the ISM, where it dominates all other processes. Combining the new calculations, we have constructed annihilation spectra for each phase of the ISM, considering various grain contents, as well as an overall combined spectrum for the ISM as a whole.
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