Tritium is a radionuclide that will be used and produced in fusion reactors. The tritium toxicity is well known but its health consequences are more difficult to assess, due to difficulties for assessing doses and to the very few cases of contamination occurred from years. The assessment of risks resulting from tritium exposure is based on ICRP models that enable the calculation of doses in tissues, by the means of a weighting factor WR, based on the relative biological effectiveness of the various radioactive emissions. Some authors are currently asking for a revision of the weighting factor to be used for the beta emission of tritium, based on its potential incorporation into DNA. A review of the many works performed on this subject shows that the relative biological effectiveness of tritium is not so different from that of gamma emissions, which are taken as reference radiations. This is in favour of keeping the current weighting factor of 1 for beta emissions of tritium, that was initially proposed and then reaffirmed by the ICRP.