The C-H activation reactions of methane by MCp(CO) (Cp = C5H5) for the metals cobalt, rhodium, and iridium have been studied using a variety of methods including a recently developed scaling scheme, different perturbation theory methods, and also hybrid density functional theory methods. The main chemical problems investigated include the recent finding that CoCp(CO) is entirely inert toward alkanes in contrast to the corresponding rhodium and iridium systems. Comparisons are made for CoCp(CO) between the reaction with methane and the reaction with CO, which is found experimentally to proceed fast. Also studied are the isotope effects on the reaction in relation to other recent experiments. At the highest level of treatment, good agreement is found with all present observations for these systems, but it should be pointed out that precise experimental information is lacking for many of the systems studied. Severe deviations between the results obtained at different computational levels are pointed out.