Despite remarkable progress over the past 5 years, estimation of high- dimensional structure, such as in graphical modeling, cluster analysis or variable selection in (generalized) regression, remains difficult. Among the main problems are: (i) the choice of an appropriate amount of regularization; (ii) a potential lack of stability of a solution and quantification of evidence or significance of a selected structure or of a set of selected variables. We introduce the new method of stability selection which addresses these two ma jor problems for high-dimensional structure estimation, both from a practical and theoretical point of view. Stability selection is based on sub- sampling in combination with (high-dimensional)selection algorithms. As such, the method is extremely general and has a very wide range of ap- plicability. Stability selection provides finite sample control for some error rates of false discoveries and hence a transparent principle to choose a proper amount of regularization for structure estimation or model selection. Maybe even more importantly, results are typically remarkably insensitive to the chosen amount of regularization. Another property of stability selection is the empirical and theoretical improvement over pre-specified selection meth- ods. We prove for randomized Lasso that stability selection will be model selection consistent even if the necessary conditions needed for consistency of the original Lasso method are violated. We demonstrate stability selection for variable selection, Gaussian graphical modeling and clustering, using real and simulated data. This is joint work with Nicolai Meinshausen.