A number of problems in Statistics and Learning Theory, such as regression and classification, can be formulated as risk minimization over a linear span of a large dictionary of given functions. Several methods have been developed to find a "sparse" solution of such a problem (provided that it exists). One of these methods is penalized empirical risk minimization with $\ell_1$-norm of the vector of coefficients used as a penalty. Another method is so called "Dantzig Selector" recently introduced by Candes and Tao. We will discuss several oracle inequalities
that express "adaptivity" of these methods to unknown sparsity of the problem.