Phenomenological impact of the resummation of logs of alpha in heavy quarkonium

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Here we would like to review recent progress on the resummation on logarithms of $α_s$ in heavy quarkonium. We will mainly focus on the phenomenological relevance of these achievements. Determinations of the $η_b(1S)$ mass, $B_c(1S)$ hyperfine splitting, inclusive electromagnetic decays and implications for $t$-$\bar t$ production near threshold.
8 pages, 8 figures, talk given at the 11th International Conference in Quantum ChromoDynamics (QCD04), Montpellier, France, 5-9 Jul 2004

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