This is the second volume in a subseries of the Lecture Notes in Mathematics called Levy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Levy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics in the area of Levy processes. The first article by Serge Cohen reviews the most important findings on fractional Levy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Levy processes, including an extensive numerical overview.