A remarkable number of reactions between neutral free radicals and neutral molecules have been shown to remain rapid down to temperatures as low as 20 kelvin. The rate coefficients generally increase as the temperature is lowered. We examined the reasons for this temperature dependence through a combined experimental and theoretical study of the reactions of O(3P) atoms with a range of alkenes. The factors that control the rate coefficients were shown to be rather subtle, but excellent agreement was obtained between the experimental results and microcanonical transition state theory calculations based on ab initio representations of the potential energy surfaces describing the interaction between the reactants.