The first article in this Survey and Review section, “From Euler, Ritz, and Galerkin to Modern Computing,” by Martin Gander and Gerhard Wanner, gives a fascinating historical account of the ideas that paved the way to finite-element-style computation. The names of Ritz, Galerkin, Bubnov, and Timoshenko have been closely associated with these methods. So too, with less justification, has that of Rayleigh. The authors take us back to the work of Euler and Lagrange on variational problems, and thereby set the scene for the classic work “through which Ritz achieved immortality.” The authors not only pepper their discussions with well-chosen illustrations and quotes, but also revisit the hand computations of Walther Ritz, so that we can marvel at the levels of persistence and ingenuity required. (Who would have guessed that Ritz came up with iterative methods for matrix eigenvalues and eigenvectors?) The survey then traces the influence of Ritz's work through to the development of modern finite element methods, where hat functions took over from eigenfunctions, polynomials, sines, and cosines. It is also worth pointing out that nowadays finite-dimensional approximations are typically viewed solely as a means to develop numerical methods. In section 9.1 of this article we learn that in Euler's time they also served as theoretical and conceptual building blocks; Euler used a finite element approach to derive a variational PDE. This article has something to offer for any reader interested in the evolutionary history of computational mathematics. The second article, “Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints,” by Qiang Du, Max Gunzburger, Rich Lehoucq, and Kun Zhou, covers some similar themes---deriving differential equations from physical principles and developing numerical approximations through a variational framework. However, the equations that arise are much less familiar. The authors discuss an intriguing new approach based on nonlocal diffusion, using the notion that fluxes, or “interactions,” may operate between regions that do not share a common boundary. The nonlocal vector calculus tools surveyed here are presented in a way that mimics the usual physical and mathematical developments for the traditional local diffusion case. This provides a unified setting for modeling, analysis, and simulation, with many of the recently proposed anomalous diffusion models from continuum mechanics arising as special cases. From the microscopic stochastic perspective, symmetric jump processes replace the more standard Brownian motion. This work will be of interest to SIAM Review readers wishing to learn about new developments in anomalous diffusion and related fields from an applied and computational mathematics perspective.