  We discuss how the works of Yves Meyer, together with Raphy Coifman, on
Calder{\'o}n's program and singular integrals with minimal smoothness in the
seventies, paved the way not only to a solution to Kato's conjecture for square
roots of elliptic operators, but also to major developments in elliptic and
parabolic boundary value problems with rough coefficients on rough domains.
