This is a personal account of the development of our buffer-gas positron trap and the new generation of cold beams that these traps enabled. Dick Drachman provided much appreciated advice to us from the time we started the project. The physics underlying trap operation is related to resonances (or apparent resonances) in positron-molecule interactions. Amusingly, experiments enabled by the trap allowed us to understand these processes. The positron-resonance "box score" to date is one resounding "yes," namely vibrational Feshbach resonances in positron annihilation on hydrocarbons; a "probably" for positron-impact electronic excitation of CO and NZ;an d a "maybe" for vibrational excitation of selected molecules. Two of these processes enabled the efficient operation of the trap, and one almost killed it in infancy. We conclude with a brief overview of further applications of the trapping technology discussed here, such as "massive" positron storage and beams with meV energy resolution.