Several recent research efforts have focused on the dynamic aspects of software architectures providing suitable models and techniques for handling the run-time modification of the structure of a system. A large number of heterogeneous proposals for addressing dychitectures at many different levels of abstraction have been provided, such as programmable, ad-hoc, self-healing and self-repairing among others. It is then important to have a clear picture of the relations among these proposals by formulating them into a uniform framework and contrasting the different verification aspects that can be reasonably addressed by each proposal. Our work is a contribution in this line. In particular, we map several notions of dynamicity into the same formal framework in order to distill the similarities and differences among them. As a result we explain different styles of architectural dynamisms in term of graph grammars and get some better insights on the kinds of formal properties that can be ...