"Unobserved heterogeneity and endogeneity are prevalent notions throughout econometrics. Most of the literature focuses on scalar unobserved heterogeneity. It implies strong restrictions on the heterogeneity of the behaviour of economic agents. This is the case in a binary treatment effect model where scalar unobserved heterogeneity and additive separability of the index in the selection equation are equivalent to the restrictive monotonicity assumption. Nonparametric random coefficients models allow for multiple sources of unobserved heterogeneity and are in line with structural economics. They are also benchmark nonseparable models and can be generalized in various ways. Due to unobserved heterogeneity, but also simultaneity or error in variables, structural models usually involve as well endogenous regressors.Nonparametric models of unobserved heterogeneity and estimation by instrumental variables usually give rise to ill-posed inverse problems. High-dimensional methods are a new set of tools that are increasingly popular in econometrics and allow handling new data configurations with many more potential regressors than observations. They are based on convex relaxation, linear or conic programming ideas, or MCMC algorithms. When the model is well approximated by a parsimonious model where many coefficients are zero they can usually estimate the parameter as well as an oracle who would know the best sparse approximation. They also offer new tools for adaptive nonparametric estimation. Some recent developments are concerned with hidden structured sparsity (structural breakpoints or other patterns other than zeros). This research proposal is on the development of a general framework and new inference tools for flexible models – nonparametric or high-dimensional – with multiple sources of unobserved heterogeneity and endogeneity in various models from economics, in particular: programme evaluation, consumer demand, demand for differentiated products, games, etc."