The two papers in this issue share a common concern: smoothing. In the first paper, it is time series that are being smoothed, and in the second paper it is multigrid methods that do the smoothing for PDE-constrained optimization problems. In biology, medicine, finance, economics, geophysics, and social sciences one frequently needs to discern “trends” in data sets. Mathematically, this problem is known as filtering, smoothing, or time series analysis, and many different methods have been devised, including moving average filters, bandpass filters, and smoothing splines. For a given set of scalars $y_t$, one wants to find another set of scalars $x_t$ that vary smoothly, but that are close to the original set. The new points $x_t$ are considered to represent the underlying trend. The question now is, how do we define what it means to “vary smoothly”? Seung-Jean Kim, Kwangmoo Koh, Stephen Boyd, and Dimitry Gorinevsky answer this question in the one-norm. In their paper “$\ell_1$ Trend Filtering,” they minimize an expression containing a one-norm, so that the resulting $x_t$ are points of a piecewise linear function. The minimization is formulated as a convex quadratic program and solved by an interior point method. This paper should be of interest to many readers, because of its connections to $\ell_1$ regularization in geophysics, signal processing, statistics, and sparse approximation. In their paper “Multigrid Methods for PDE Optimization,” Alfio Borzì and Volker Schulz review multigrid methods for solving infinite-dimensional optimization problems whose constraints are expressed in terms of partial differential equations (PDEs). Such optimization problem arise in optimal control, shape design, and shape optimization. Multigrid methods, very informally, solve PDEs by discretizing them iteratively on a hierarchy of grids, so as to capture all frequencies. So-called smoothers are responsible for high frequencies, while lower frequencies are resolved on coarser grids. This paper is essentially self-contained. It starts by introducing terminology for PDE-constrained optimization problems and reviewing multigrid methods. Subsequent discussions focus on multigrid SQP, Schur-complement-based multigrid smoothers, and collective smoothing multigrid, as well as applications to optimal control problems governed by hyperbolic, elliptic, and parabolic PDEs.