I will describe recent advances in the so called conformal and S-matrix bootstrap programs whereby we constrain the space of possible QFTs by imposing a myriad of basic physical principles from unitarity to Lorentz invariance and analyticity. I will survey various applications which range from critical systems such as those relevant for the study of phase transitions as in boiling water as well as gapped theories all the way from integrable theories in two dimensions to non-perturbative dynamics of flux tubes and pions in four dimensions.