Beckner's inequality is a series of inequalities indexed by a parameter between 1 and 2 which interpolate between the Poincare inequality and the logarithmic Sobolev inequality, originally proved for the standard Gaussian measure. I will discuss this inequality in various settings, from the very simple two point distribution to the path space over a compact Riemannian manifold and show the rich content of this inequality in relation to probability theory and, in particular, stochastic analysis.