We consider the problem of identification of time-varying, and nonlinear systems from measurements of its inputs and outputs over a chosen time frame. We present the rational maps in the time, frequency, and correlation domain as an effective way of identifying such systems. As we show, their use leads to computationally efficient algorithms while providing great flexibility in capturing complex phenomena. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licneses/by-nc-nd/4.0/)