  We present a review of methods for optimal experimental design (OED) for
Bayesian inverse problems governed by partial differential equations with
infinite-dimensional parameters. The focus is on problems where one seeks to
optimize the placement of measurement points, at which data are collected, such
that the uncertainty in the estimated parameters is minimized. We present the
mathematical foundations of OED in this context and survey the computational
methods for the class of OED problems under study. We also outline some
directions for future research in this area.
