Positron traps have the capability for producing high-quality positron beams and intense positron pulses for a variety of scientific and technological applications including atomic physics experiments and probes for materials science. Trap-based beams offer advantages over conventional positron beam systems, including the ability to produce ultracold positron beams, giant positron pulses, ultra short pulses, and high-efficiency brightness enhancement schemes. Techniques for accumulating positrons in traps and manipulating them before release are described, including bunching and compression.