Correlated measurements of the individual positron lifetimes (= positron ages) and of the momenta of the annihilating positron-electron pairs (Age-Momentum Correlation, AMOC) using an MeV positron beam make positron annihilation experiments feasible which hardly could be performed by other techniques. Two examples are given: (i) A novel metastable ortho-positronium state and the transition to a second longer lived state was found in liquid Ar and Kr which shows that positronium is formed before being trapped in self-localized states (positronium bubbles). (ii) For all positronium forming solids and liquids investigated so far epithermal positronium and its slowing-down could be observed, indicating that no special sites are required for its formation. The positronium slowing-down times vary form 10 ps to 40 ps in liquids and solids where optical phonons are present. In liquid and solid rare gases where optical phonons are absent and energy can be transferred to acoustical phonons only, much higher slowing-down times (up to 400-600 ps) are found.