Abstract: Cold molecular ions, especially those confined in ion traps, have novel properties such as high localization, long storage time and isolation from noisy environments. Because of this, spatially trapped cold molecular ions have attracted ever increasing attention as a promising candidate for precision molecular spectroscopy and fundamental studies of ionneutral collisions. The field of cold molecular ions has developed very fast in recent years. In this paper we will introduce the methods for generating cold and trapped molecular ions, and also the latest results of the applications of cold and trapped molecular ions in precision measurements and molecular collisions at very low temperatures.