Phenomenological impact of the resummation of logs of α in heavy quarkonium *

Here we would like to review recent progress on the resummation on logarithms of αs in heavy quarkonium. We will mainly focus on the phenomenological relevance of these achievements. Determinations of the ηb(1S) mass, Bc(1S) hyperfine splitting, inclusive electromagnetic decays and implications for t-t production near threshold.