This special issue contains selected papers of the 21st International Conference on Rewriting Techniques and Applications (RTA 2010) which was held from July 11 to July 13, 2010, in Edinburgh, Scotland as part of the 5th International Federated Logic Conference (FLOC 2010).

RTA is the major forum for the presentation of research on all aspects of rewriting. Previous RTA conferences were held in Dijon (1985), Bordeaux (1987), Chapel Hill (1989), Como (1991), Montreal (1993), Kaiserslautern (1995), Rutgers (1996), Sitges (1997), Tsukuba (1998), Trento (1999), Norwich (2000), Utrecht (2001), Copenhagen (2002), Valencia (2003), Aachen (2004), Nara (2005), Seattle (2006), Paris (2007), Hagenberg (2008) and Brasilia (2009).

Six of the twentythree papers presented at the conference were invited to submit an extended version to this special issue, and five of those papers were finally accepted for inclusion in this special issue, including "Partial Order Infinitary Term Rewriting" by Patrick Bahr, who was given the award for Best Contribution to RTA 2010 for his two papers. Each submitted paper was refereed by at least two expert referees.

My thanks go to the members of the Program Committee of RTA 2010 and their subreferees, as well as to all those who served in addition as reviewers for this special issue. I would also like to thank Benjamin Pierce, who was Managing Editor of LMCS, for having invited me to edit this special issue, and for his assistance and guidance.