An overview is presented of current techniques to accumulate and cool large numbers of positrons from a radioactive Na-22 source and neon moderator, and the first operation of a new generation of positron accumulator is described. Experiments are discussed that use these techniques to study the interaction of positrons with atoms and molecules at low energies (i.e,, below the threshold for positronium formation), including systematic studies of the dependence of positron annihilation on chemical composition. By measuring the Doppler-broadening of gamma-ray annihilation radiation, the quantum state of the annihilating electrons in atoms and molecules was identified. These experiments indicate that positrons annihilate with approximately equal probability on any valence electron. Annihilation with inner shell electrons is infrequent, but is measurable at the level of a few percent in heavier atoms. Measurements of annihilation rates in molecules as a function of positron temperature revealed a number of interesting trends that are briefly discussed. We have developed a new technique to make a cold, bright positron beam. This technique is now being used for a new generation of scattering experiments in the range of energies less than or equal to 1 eV. Other possible experiments to study aspects of atomic and molecular physics using positron accumulation techniques and this cold positron beam are briefly discussed. (C) 2000 Elsevier Science B.V. All rights reserved.