This review describes advances which have occurred during the past decade i
n chemical reaction dynamics using crossed molecular beams. After a brief h
istorical introduction, advances in the generation and state selection of b
eams of reactants, and in the schemes for product detection, which are at t
he basis of our increased ability to measure state-averaged and state-resol
ved reactive differential cross sections in crossed beam experiments, an de
scribed. The novel couplings of laser and synchrotron radiation to these ex
periments are noted. A selection of case studies are considered in some det
ail, to exemplify recent improvements in our understanding of gas-phase neu
tral reaction dynamics. The examples include prototype reactions involving
three-atom and four-atom systems, and the results are discussed in the ligh
t of the most recent, synergistic, theoretical developments for treating bo
th the potential energy surfaces and the reaction dynamics. Progress made i
n studies of reactions of molecular radicals and of chemically important at
oms, such as carbon, nitrogen, and oxygen, with polyatomic molecules, as ma
de possible by recent developments in the classic crossed beam technique wi
th mass spectrometric detection, is emphasized. Some complementary techniqu
es that recently have contributed to our understanding of chemical reactivi
ty are also described briefly.