Eigenvalues play an important role in many fields of applied mathematics to engineering. For some applications it may be desirable to calculate the variables of a model in order to optimize an objective function and/or to verify constraints that involve the eigenvalues of a certain matrix. In general the elements of such a matrix depend nonlinearly on the optimization variables. Despite its potential to address diverse chemical engineering problems, eigenvalue optimization techniques have not been extensively used in the Process Systems Engineering discipline. The objectives of this contribution are to review most relevant topics on eigenvalue optimization and to present formulations and solution strategies to practically address eigenvalue optimization problems in the field of chemical engineering. In order to illustrate the ideas, several small size applications, which have to do with the analysis and control of nonlinear dynamic systems, are developed. Other potential applications and future lines of research are also suggested. (c) 2007 Elsevier B.V. All rights reserved.