Chemistry and cooling in metal-free and metal-poor gas

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.