Atomic defects as, e.g., vacancies and structural phase transitions play an important role in solid state physics. In the present review paper we first demonstrate that vacancies in the compound semiconductor SiC can be selectively introduced on the C or the Si sublattices and specifically detected by employing positron lifetime spectroscopy and coincident measurements of the Doppler broadening of the positron-electron annihilation radiation. In addition these techniques are shown to be most useful for studying structural phase transitions in complex solids on an atomic level as demonstrated in the case of decagonal Al(71),(5)Ni(14),(5)Co(14) quasicrystals.