Although the theory of contextual grammars is about thirty years old and, as one can see in the previous chapters, this theory is pretty well developed, many problems still wait for further research efforts. Some of them are “local” technical problems, others are research topics of a larger interest. We list here a number of problems stated already in this book; in most cases, we reformulate them in a more general form. Of course, not all of them have the same importance (hence not all of them deserve the same interest). In our opinion, of primary interest are those questions related to possible applications of contextual grammars as models of natural or artificial languages syntax and those problems related to characterizations of recursively enumerable languages. The interest for the first research direction is obvious, the second one can shed a new light on the “structure” of computability: Chomsky grammars, Turing machines, Markov normal algorithms, Thue and Post systems, etc, are basically *rewriting mechanisms*; contextual grammars (as well as computing devices appearing in the DNA computing area, such as splicing systems) are not using rewriting, but *adjoining* operations; still, they characterize *RE* as soon as some erasing possibilities are provided. And, it seems, the nature uses mainly such adjoining, cut-and-paste (splicing), insertion, and deletion operations when “computing” (see the genetic area).