The real structured $\epsilon$-pseudospectrum of a real matrix A consists of the eigenvalues of all real matrices that are $\epsilon$-close to A.In this talk,we will introduce a criss-cross method to compute the rightmost point in the real pseudospectra.This method is based on a superset characterization of real pseudospectra,and it has proven global convergence.In the second part of the talk,we will combine criss-cross with a subspace projection scheme to solve large-scale problems.This leads to a locally superlinearly convergent algorithm.The same subspace framework can also be extended to large scale univariate eigenvalue optimization.There we can show more: the convergence order will be 1+\sqrt{2}.A number of numerical experiments confirm our theoretical results and reveal that the established convergence order appears to be tight.