I will present in this talk use cases in ML where optimal matchings pop up in various applied areas in ML. I will in particular mention areas where the optimal matching needs to be differentiated, in a way or another w.r.t. input parameters. I will then introduce two approaches to do so, either through entropic regularization or using neural solvers. I will present the implementation of these approaches in two instances: in the ott-jax toolbox that I have been developing actively, or to solve a bilevel optimization problem that appears when fitting JKO models to time series of measures.