We review our recent results on higher order corrections in positronium physics. We discuss a calculation of the recoilO(m&agr;6)corrections to the hyperfine splitting [1] and energy levels [2] of a positronium atom,O(m&agr;7&hthinsp;ln2&hthinsp;&agr;)contributions to the positroniumS-wave energy levels [3] andO(&agr;2)radiative corrections to the parapositronium decay rate [4]. ©2000 American Institute of Physics.