Full waveform inversion (FWI) is a data-fitting inverse problem aiming to delineate high-resolution quantitative images of the Earth.While its basic principle has been proposed in the eighties,the approach has been significantly developed and applied to 2D and 3D problems at various scales for the last fifteen years.Despite these successes,FWI is still facing some issues for applications in complex geological setups because of some lack of robustness and automatic workflow,while being computationally intensive.In this paper,after a short review of the basic FWI formulation and analysis of the FWI gradient,three recent methodological developments performed in the frame of the SEISCOPE project are presented.First,an algorithmic development is presented as a low-memory and computationally efficient approach for building the time-domain FWI gradient in 3D viscous media.Second,a reformulation of FWI is performed to handle reflections in their tomography regime while still using the diving waves,leading to the joint full waveform inversion (JFWI) approach.Finally,an optimal transport approach is proposed as an alternative to the classical difference-based misfit for mitigating the cycle-skipping issue.