The idea that ice and other trapped volatiles exist in permanently shadowed regions near the lunar poles was proposed by Watson, Murray, and Brown <1961>. It is reexamined in the present paper, in the light of the vast increase of our lunar knowledge. The stability of the traps and the trapping mechanism are verified. Four potential sources of lunar H2O, (1) solar wind reduction of Fe in the regolith, (2) H2O-containing meteoroids, (3) cometary impact, and (4) (the least certain) degassing of the interior, can supply amounts of trapped H2O estimated in the range of 1016--1017 g. Two important destructive mechanisms have been identified: photodissociation of H2O molecules adsorbed on the sunlit surface sputtering or decomposition of trapped H2O by solar wind particles. The effect of impact gardening is mainly protective. The question of the presence of H2O in the traps remains open; it can be settled by experiment.