We highlight some recent work from our laboratory on reactions of atoms and radicals with simple molecules by the crossed molecular beam scattering method with mass-spectrometric detection. Emphasis is on three-atom (Cl + H2) and four-atom (OH + H2 and OH + CO) systems for which the interplay between experiment and theory is the strongest and the most detailed. Reactive differential cross sections are presented and compared with the results of quasiclassical and quantum mechanical scattering calculations on ab initio potential energy surfaces in an effort to assess the status of theory versus experiment.