The Principles of Advanced Discrete Simulation (PADS) special issue is based on the selected papers from the 2015 ACM SIGSIM-PADS Conference, which is the flagship conference of the ACM's Special Interest Group on Simulation and Modeling (SIGSIM). Building on the 29 years of history and the reputation for high-quality papers, the 2015 ACM SIGSIM-PADS Conference was held at the University of Westminster in London on June 15-17, 2015. The guest editors of this special issue served as the conference General Chair (Simon Taylor) and the Co-Program Chairs (Navonil Mustafee and Young-Jun Son) and were responsible for the proceedings of the conference. The peer-review process for the special issue built on to the original reviews for the conference, wherein the submitted papers were reviewed by members of the SIGSIM-PADS International Program Committee, with most papers receiving three referee reports and follow on discussions. A total of 24 submissions were accepted and published as full papers in the proceedings [Taylor et al. 2015]. Of these, the authors of the top 12 papers selected by the guest editors together with the editor-in-chief (EIC) of TOMACS were invited to submit a substantially extended version of their work to the special issue. Prior to the review process being started, the guest editors requested the authors to prepare a document outlining changes and extensions to their original ACM SIGSIM-PADS 2015 submission, and which also took into account the reviewer comments received for the conference submission. The guest editors then considered the changes and requested clarification to the authors, if required. During the review process, the referees were sent the authors' outline plans for paper extension; the referees were requested to check that the submitted special issue paper included the extensions and revisions that were planned by the authors. The special issue papers were peer-reviewed by a minimum of three reviewers. Most underwent two rounds of reviews, with two papers undergoing an additional review cycle. We have one paper that has undergone the Replicating Computational Results (RCR) review process [Helms et al. 2017]. The RCR review is included in this issue [Hillston 2017]. Two articles, from the original shortlist of 12, are still under review. Keeping in mind the timescales for publication, we decided, in consultation with the EIC, that those two papers will be published in a regular issue if accepted. The special issue consists of eight articles. The focus of the first two articles is on the application area of cell biology. The article by Lin et al. [2017] reports the development of an optimistic and thread-based parallel discrete event simulator (PDES), called the Neuron Time Warp-Multi Thread (NTW-MT), for stochastic simulation of chemical reactions in cells. The contribution of the article is the NTW-MT, which can be used for the simulation of reaction diffusion models of neurons. The second article is also related to cell biology, but its focus is on modeling formalisms. It contri...