Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by the fact that one-dimensional multiexponential modeling is an ill-posed inverse problem with substantial ambiguities. In this paper, we present an overview of a recent multidimensional correlation spectroscopic imaging approach to this problem. This approach helps to alleviate ill-posedness by leveraging multidimensional contrast encoding (e.g., 2D diffusion-relaxation encoding or 2D relaxation-relaxation encoding) combined with a regularized spatial-spectral estimation procedure. Theoretical calculations, simulations, and experimental results are used to illustrate the benefits of this approach relative to classical methods. In addition, we demonstrate an initial proof-of-principle application of this kind of approach to in vivo human MRI experiments.