Positron annihilation (PA) studies in zeolites show the coexistence of several annihilation channels. Up to seven lifetimes, from 0.13 ns to 142 ns, with intensities of the long-lived components reaching 30 %, can be resolved, their number and significance being limited by statistical accuracy and ill-defined data fitting. The longest lifetimes denote low interaction of orthopositronium, o-Ps, with its surroundings. PA parameters from positron lifetime or Doppler spectroscopy applied to zeolite samples (whether substituted or not) depend on the preparation mode, the presence of adsorbed gases, water, impurities, etc. A good agreement for the long-lived components, ascribed to trapped o-Ps states localized in various extra and intra-structural open sites, is obtained through the Eldrup model. Correct characterization of these components requires corrections for the 3gamma/2gamma counting efficiency ratio. It is concluded that o-Ps trapping poses a limitation to the applicability of PA to structural investigation in porous systems.