The PAX collaboration has proposed an experimental program with
polarized antiprotons at the new "Facility for Antiproton and Ion
Research" (FAIR), to be built at GSI (Darmstadt, Germany) during the next decade. The physics case for experiments with polarized antiprotons is outstanding and covers e.g.: (i) the investigation of nucleon spin structure ("transversity") via the Drell-Yan process, (ii) measurements of electromagnetic form factors in the time-like region, and (iii) double-polarized proton-antiproton hard scattering. There are, however, major technological challenges to be met in order to produce polarized antiprotons - foremost is the question of how to polarize antiprotons effectively. In my talk, I will discuss the ideas of how to achieve this goal and what is currently done as preparatory tests and measurements at COSY-Jülich and elsewhere.