We describe Direct Simulation Monte Carlo (DSMC) methods which model s
ystems under low pressure with emphasis on the treatment of molecular
collisions in DSMC methods. According to the treatment of molecular co
llisions, several variants of DSMC methods can be distinguished. This
work compares some versions of DSMC methods (Bird's time counter, no t
ime counter, Babovsky's, Nanbu's, Koura's null collision technique. Ya
nitskiy's, Abe's and direct (Kac's) methods).