The fast reaction between C(P-3) and C2H2 is thought to be an important process in dense interstellar clouds as. it provides a mechanism for the growth of carbon chains. This feature article describes a complementary series of recent experimental and theoretical investigations on this reaction. This includes kinetic measurements of rate constants at low temperatures and crossed molecular beam determinations of integral and differential cross sections. The theory employs first-principles electronic structure computations and wave packet dynamics to calculate cross sections and rate constants for forming the linear and cyclic isomers of C3H which can be formed in the reaction. The rate constant and cross section measurements show that there are no barriers in the potential surface for the reaction, whereas the differential cross section experiments provide new evidence for the formation of C-3 + H-2 products. The theoretical results of overall rate constants and cross sections agree quite well with the experiments, and it is predicted that the linear isomer of C3H should be formed preferentially at low temperatures.