Abstract: The objective of linguistic dynamic systems is to use computing with words for effective utilization of information at a linguistic level, and for modeling, analysis, control, and evaluation of complex systems. The main idea in research of linguistic dynamic systems is to establish its own theoretic foundation by adopting useful and well-established concepts, frameworks, and methods in conventional dynamic systems. Major applications of linguistic dynamic systems include abstraction and linguistic analysis of conventional dynamic systems, dynamic analysis, decision synthesis, and policy evaluation of economic, social, political, management, and ecological systems at certain linguistic levels, as well as knowledge mining and dynamic representation of huge data sets in knowledge engineering. Our goal is to develop a bridge between human linguistic knowledge representation and computer digital knowledge representation, and make it as one of the solid theoretic foundations for next-generation of intelligent human machine interfaces and knowware systems. This paper addresses several fundamental issues in recent research of linguistic dynamic systems.