In a nutshell, this special issue of The Journal of Applied Non-Classical Logics consists of revised and extended versions of papers which are among the best presented at WCP III (Third World Congress on Paraconsistency) held on July 28-31, 2003 in Toulouse, France. A class of logics is usually named in one of two ways. One is to describe what the logics in the class are about. For instance, ``epistemic logics'' is the name for a class of logics which deal with reasoning about knowledge. The other possibility is to indicate a technical criterion which is specific of the logics in the class. For instance, ``modal logics'' is the name for a class of logics which admit at least one modal operator, that is, an operator which is not truth-functional. (Of course, some logics can be in two classes named in each way.) As to what is to be of interest here, ``paraconsistent logics'' seems to be a name of the second kind (although it might be argued that they are about reasoning from inconsistent premises). The main implication is that the range of paraconsistent logics is really broad, not only on the count of technical aspects but also by the fact that the objectives may originally have little to do with the idea of ``not deducing each and every formula from a contradiction''. So is the range of the papers in this special issue, as appears from the table of contents of this special issue.