Rate coefficients are calculated using canonical variational transition state theory with multidimensional tunneling (CVT/SCT) for the reactions H + H2O2 --> H2O + OH (1a) and H + H2O2 --> HO2 + H2 (1b). Reaction barrier heights are determined using two theoretical approaches: (i) comparison of parametrized rate coefficient calculations employing CVT/SCT to experiment and (ii) high-level ab initio methods. The evaluated experimental data reveal considerable variations of the barrier height for the first reaction: although the zero-point-exclusive barrier for (1a) derived from the data by Klemm et al. (First Int. Chem. Kinet. Symposium 1975, 61) is 4.6 kcal/mol, other available measurements result in a higher barrier of 6.2 kcal/mol. The empirically derived zero-point-exclusive barrier for (1b) is 10.4 kcal/mol. The electronic structure of the system at transition state geometries in both reactions was found to have "multireference" character; therefore special care was taken when analyzing electronic structure calculations. Transition state geometries are optimized by multireference perturbation theory (MRMP2) with a variety of one-electron basis sets, and by a multireference coupled cluster (MR-AQCCSD) method. A variety of single-reference benchmark-level calculations have also been carried out; included among them are BMC-CCSD, G3SX(MP3), G3SX, G3, G2, MCG3, CBS-APNO, CBS-Q, CBS-QB3, and CCSD(T). Our data obtained at the MRMP2 level are the most complete; the barrier height for (1a) using MRMP2 at the infinite basis set limit is 4.8 kcal/mol. Results are also obtained with midlevel single-reference multicoefficient correlation methods, such as MC3BB, MC3MPW, MC-QCISD/3, and MC-QCISD-MPWB, and with a variety of hybrid density functional methods, which are compared with high-level theory. On the basis of the evaluated experimental values and the benchmark calculations, two possible recommended values are given for the rate coefficients.