The spectrum of fundamental absorption of direct-gap semiconductors such as gallium arsenide (GaAs) and cadmium sulfide (CdS) is continuous and corresponds to band-to-band transitions. It begins with transitions at the center of the Brillouin zone, k = 0 . In a perfect crystal, this spectrum is preceded by a hydrogen-like series of the transitions to s -states of Wannier-Mott excitons. In addition to the exciton lines, there are surprisingly strong additional absorption lines in the same spectral region. They belong to excitons weakly bound to impurities and defects and are termed 'impurity excitons'. Anomalously high intensity of the impurity-exciton lines indicate their giant oscillator strength of about f i ∼ ∼ 10 per impurity center while the oscillator strength of free excitons is only of about f e x ∼ ∼ 10 − − 4 per unit cell. Shallow impurity-exciton states are working as antennas borrowing their giant oscillator strength from vast areas of the crystal around them. They were predicted by Emmanuel Rashba first for molecular excitons and afterwards for excitons in semiconductors. Giant oscillator strengths of impurity excitons endow them with ultra-short radiational life-times τ τ i ∼ ∼ 1 ns.