This review describes advances which have occurred during the past decade in chemical reaction dynamics using crossed molecular beams. After a brief historical introduction, advances in the generation and state selection of beams of reactants, and in the schemes for product detection, which are at the basis of our increased ability to measure state-averaged and state-resolved reactive differential cross sections in crossed beam experiments, are described. The novel couplings of laser and synchrotron radiation to these experiments are noted. A selection of case studies are considered in some detail, to exemplify recent improvements in our understanding of gas-phase neutral reaction dynamics. The examples include prototype reactions involving three-atom and four-atom systems, and the results are discussed in the light of the most recent, synergistic, theoretical developments for treating both the potential energy surfaces and the reaction dynamics. Progress made in studies of reactions of molecular radicals and of chemically important atoms, such as carbon, nitrogen, and oxygen, with polyatomic molecules, as made possible by recent developments in the classic crossed beam technique with mass spectrometric detection, is emphasized. Some complementary techniques that recently have contributed to our understanding of chemical reactivity are also described briefly.