We study high-dimensional linear models with error-in-variables. In addition to handle the high dimensionality of the parameters, these models are challenging because of the need to account for measurement errors to avoid non-vanishing biases and its impact on regularization parameters. A recent growing literature has proposed various estimators that achieve good rates of convergence. In this talk we first propose a new estimator which main feature is that the choice of penalty parameters is pivotal even in the presence of heteroskedastic errors. Importantly, we show how to cast the computation of the estimator as the solution of a convex program with second order cone constraints which allows the use of algorithms with theoretical guarantees and reliable implementation. Second, we construct simultaneous confidence regions for the parameters of interest in such high-dimensional linear models with error-in-variables. These confidence regions are based on the construction of moment conditions that have an additional orthogonal property with respect to nuisance parameters. We provide a construction that requires us to estimate an additional high-dimensional linear model with error-in-variables for each component of interest. We use a multiplier bootstrap to compute critical values for simultaneous confidence intervals for a subset S of the components. We show its validity despite of possible model selection mistakes, and allowing for the cardinality of S to be larger than the sample size. (Based on joint works with V. Chernozhukov, A. Koul, M. Rosenbaum and A. Tsybakov.)