Pseudospectra and structured pseudospectra are subsets of the complex plane which give a geometric representation, via eigenvalues, of the effects of perturbations to a matrix. We survey the historical development of the subject, and the definitions and characterizations of the various sets of pseudospectra. Motivated by the fact that a nonnormal matrix in the 2-norm can become normal in a different norm, we describe a numerical investigation into the question of characterizing which perturbations have the greatest effect on the eigenvalues of the matrix
