The 2013 SIAM Conference on Computational Science and Engineering (CS&E) was held February 25--March 1, 2013, in Boston, Massachusetts. The SIAM Journal on Scientific Computing (SISC) created this special section in association with the CSE13 conference. Of course, the topic of CS&E is quite broad, so this special section focuses on two important themes: Planet Earth and Big Data. These topics are in the forefront of many contemporary discussions. Recently, “Mathematics, Statistics, and the Data Deluge” and “Mathematics of Sustainability” were the themes of the Math Awareness Months, in 2012 and 2013, respectively. These special months are sponsored by the Joint Policy Board for Mathematics (JPBM), which includes SIAM. Additionally, more than 100 technical organizations and institutes banded together with UNESCO to declare 2013 a special year of emphasis on the Mathematics of Planet Earth (MPE13). Of course, SISC traditionally publishes papers on these themes, and the papers in this special section are no different except that they represent a concetration in these topics. The eleven papers in this special section are a nearly even split between the two topics, with six on Planet Earth, four on Big Data, and one that intersects both themes. There are many natural intersections of the interests of SISC and Big Data. Randomized algorithms are an important approach for scaling down large-scale problems with redundant data. We include two papers on this topic. One paper provides a new way to do canonical correlation analysis for tall and skinny matrices by using a randomized algorithm to reduce the problem. The other paper considers the problem of quantile regression based on a weighted sampling method. Appealingly, both methods come with robust error bounds. MapReduce represents a new distributed computing paradigm that is data-centric, and we also have two papers on this topic. One considers a network science problem: approximate triangle counting in massive graphs. The other builds a reduced-order model from a tall and skinny matrix comprising many terabytes of data. Finally, we have a paper that has intersected both themes, using a novel approach for large-scale matrix completion with applications to exploration seismology. SISC is often an ideal venue for papers on computational aspects of geophysical phenomena, so Planet Earth is a natural theme. Six such papers appear in this special section. Three papers focus on the inverse problem of estimating unknown medium parameters. One paper tackles large-scale 3D seismic waveform inversion, introducing novel heuristics for balancing between computational cost and accuracy during the solution process. A second paper develops, analyzes, and assesses highly efficient stochastic and deterministic dimensionality reduction The third paper introduces a novel approach for imaging subsurface fluid flow by estimating the flow field and initial state directly from a time series of geophysical flow data, coupling the flow and imaging equations. We have two papers focusing on large-scale planetary flows. One develops and implements derivative-based methods of uncertainty quantification for global ocean state estimation, employing the MIT ocean general circulation model. The second paper develops a fully implicit nonhydrostatic solver for mesoscale atmospheric flows. The numerical solver employs a Jacobian-free Newton--Krylov--Schwarz algorithm, and it is implemented and run in parallel, demonstrating nearly linear scaling for thousands of processor cores. Our sixth Planet Earth paper develops a finite element solver for quasi-Newtonian flows. The paper features an analysis of the continuous saddle-point problem, and the numerical solver is demonstrated on realistic gravity flows, a viscoelastic steady wave, and glacier flow. The guest editorial board worked very hard to ensure a rigorous peer-review process while meeting deadlines. Special thanks are due to Mitch Chernoff (SIAM Publications Manager) and Brittni Holland (SIAM Editorial Associate) for their efforts on this special section.