We introduce recent developments of analysis of highly oscillatory functions. In particular we sketch methods extending conventional Fourier analysis, to unravel complex oscillations exploiting both phase and amplitudes of holomorphic functions. The miracles of nonlinear complex holomorphic analysis, such as factorization and composition of functions lead to new versions of holomorphic orthonormal bases, relating them to multiscale dynamical systems, (literally deep neural nets) obtained by composing Blaschke factors.