I will present new results in the separation of variables (SoV) program for integrable models. The SoV methods are expected to be very powerful but until recently have been barely developed beyond the simplest gl(2) models. I will describe how to realize the SoV for any gl(N) and demonstrate how to solve the longstanding problem of deriving the scalar product measure in SoV for gl(N) spin chains. Using these results I will compute a large class of correlation functions and overlaps in a simple determinant form. I will also present novel applications of SoV in 4d integrable CFT's. Based on arXiv:2103.15800, 2011.08229, 1910.13442, 1907.03788, 1610.08032.
