Why should we care about the top quark Yukawa coupling?

In the cosmological context, for the Standard Model to be valid up to the scale of inflation, the top quark Yukawa coupling $y_t$ should not exceed the critical value $y_t^{crit}$, coinciding with good precision (about 0.02%) with the requirement of the stability of the electroweak vacuum. So, the exact measurements of $y_t$ may give an insight on the possible existence and the energy scale of new physics above 100 GeV, which is extremely sensitive to $y_t$. We overview the most recent theoretical computations of $y_t^{crit}$ and the experimental measurements of $y_t$. Within the theoretical and experimental uncertainties in $y_t$ the required scale of new physics varies from $10^7$ GeV to the Planck scale, urging for precise determination of the top quark Yukawa coupling.