Some aspects of both theoretical and experimental studies of the positronium system to probe physics beyond the Standard Model are reviewed. In particular, new experiments to search for the invisible decay of orthopositronium (o-Ps) with the sensitivity in the branching ratio Br(o-Ps invisible) 10^-8-10^-7 are discussed. The experimental technique involves a specially designed high-efficiency pulsed slow-positron beam, which is also applicable for other experiments with o-Ps in vacuum. Details of the beam design as well as the first measurement results are presented. Possible applications of the pulsed slow-positron beam for materials research are discussed.

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