Visualizing and quantifying the properties of a medium using sparse indirect measurements is the final goal of all the imaging methods in different fields. In this quest, inverse theory and optimization play a decisive role in enabling such inferences from indirect and incomplete measurements. Full Waveform Inversion (FWI) has reached maturity gates and emerged as the leading seismic imaging technique in the industry and academia. Moreover, its simple fundamental principle and its flexibility around its optimization formulation make it an attractive method for various applications in different fields. In this rapidly evolving context, revisiting the fundamental concepts of FWI, elaborated several decades ago and poorly questioned since then, has appeared to be the only way towards significant breakthroughs. During my PhD, I developed a new formulation of FWI equipped with leading-edge regularizations and presented promising results in different fields of application. In this presentation, I will start with the methodological concepts of FWI and describe the challenges raised by its nonlinearity, ill-posedness and computational cost. Then, I will talk about the recently proposed methods that aim to solve some of these problems. Finally, I plan to finish my talk with some of the difficulties and open problems that we have.