Interaction of hydrogen atoms is considered with the "perfect" lattice and with isolated vacancies (V)? by means of ab initio model calculations in 3C- and 4H-SiC. We find that interstitial atomic hydrogen acts as a relatively shallow donor in 3C- and as an amphoteric trap in 4H-SiC. Only two H atoms can be accomodated by V(C) and (V(C) + nH) complexes are hole traps (n=1,2). V(Si) can in principle be saturated with W but (V(Si) + nH) complexes are electron traps for n = 1,2. We predict high concentration of mobile, compensating H(i)(+) centers in p-type material. In n-type SiC the stable form of interstitial hydrogen is H(2) (with low solubility) and the dominant hydrogen defects are (V(Si) + nH) traps. H(i) is attracted by shallow accepters and (V(Si) + H) but not by shallow donors or (V(C) + H). Spectroscopic properties of H-related defects have been calculated. We propose that the T5 center is more likely to arise from (V(C) + 2H)(+) than from V(C)(+).