Although one can formulate an intuitive notion of instantaneous frequency, generalizing "frequency" as we understand it in e.g. the Fourier transform, a rigorous mathematical definition is lacking. In this talk, we consider a class of functions composed of waveforms that repeat nearly periodically, and for which the instantaneous frequency can be given a rigorous meaning. In other words, we consider the problem of the following form: given a function $$f(t)=\sum_{k=1}^K A_k(t)s_k(\phi_k(t)),\mbox{ with } A_k(t),\phi'_k(t)>0 ~ \forall t,$$ and $s_k$ are $2\pi$ periodic, compute $s_k(t)$, $A_k(t)$ and $\phi'_k(t)$ or describe their properties from $f$. We introduce the Synchrosqueezing transforms, which can be used to determine the instantaneous frequency of functions in this class, even if the waveform is not harmonic. The properties of the Synchrosqueezing transform, like robustness to many kinds of noises, the ability to detect the dynamics of the system will also be discussed. Finally we provide examples in sleep depth detection, ventilator weaning and seasonality detection.