A summary is presented of the physical considerations governing line formation in molecular clouds with kinetic temperatures in the range from 5 to 100 K and hydrogen number densities in the range from 100 to one million per cubic centimeter. An exposition of the classical Sobolev formulation due to Goldreich and Kwan (1973) is followed by results of a simple microturbulent model with partial redistribution due to Deguchi and Kwan. It is explained how line formation theory in molecular clouds is in a somewhat unsatisfactory state. Large velocity gradient models can account for the observed line shapes, but imply collapse times that are unreasonably short (less than 10 to the 6 years). Microturbulent models give unrealistic self-absorbed CO profiles, which are scarcely improved using transfer theory which includes partial redistribution. It is hoped that the review will serve to draw the attention of practitioners of line transfer theory in stellar atmospheres to a key problem in interstellar physics that requires further attention.