  I summarize four of the most important areas of uncertainty in the study of
the chemistry and cooling of gas with zero or very low metallicity. These are:
i) the importance and effects of HD cooling in primordial gas; ii) the
importance of metal-line and dust cooling in low metallicity gas; iii) the
impact of the large uncertainties that exist in the rate coefficients of
several key reactions involved in the formation of H2; and iv) the
effectiveness of grain surface chemistry at high redshifts.
